Gemara

65b (Beraisa): If a pipe was hollowed out and then attached (it is considered a Keli), (so) it disqualifies a Mikveh. (If three Lugim of water from it fall into a Mikveh with less than 40 Se'ah of water, the Mikveh is disqualified even when it will have enough water)l

If it was attached and then hollowed out, it does not disqualify a Mikveh. (It is not considered a Keli.)

Question: This is unlike R. Eliezer, and unlike Chachamim!

(Mishnah - R. Eliezer): If a baker's board was fixed into the wall, it cannot become Tamei;

Chachamim say, it can become Tamei.

R. Eliezer considers attached Kelim like land, even if they were made and later attached. Chachamim consider attached Kelim like Metaltelim, even if they were made after they were attached!

Answer #1: The Beraisa is R. Eliezer. He is more lenient about the board, for Tum'ah of wooden Kelim without a receptacle is only mid'Rabanan.

Objection: This implies that Mayim She'uvim (water that was in a Keli) disqualifies a Mikveh mid'Oraisa. We hold that it is a Pesul mid'Rabanan!

Answer #2: Really, the Beraisa is Chachamim. They are lenient about the pipe because Mayim She'uvim disqualifies a Mikveh only mid'Rabanan.

If it was hollowed out and then attached they are stringent, for it was a Keli before it was attached.

Rishonim

Rif (Shevu'os 5b): Three Lugim of She'uvim disqualify an incomplete Mikveh. One may add She'uvim to a complete Mikveh, or to an incomplete Mikveh through Hamshachah (pouring on the ground, and it flows into the Mikveh).

Rambam (Hilchos Mikva'os 4:1,2): Mid'Oraisa one may be Tovel in "Mikve Mayim" of 40 Sa'im, whether or not it is She'uvim. Mid'Rabanan, Mayim She'uvim is Pasul for Tevilah. Further, three Lugim of She'uvim disqualifies a Mikveh. Even though it is mid'Rabanan, it is learned from a Hekesh. "Ach Mayan u'Vor Mikve Mayim Yihyeh Tahor" - Mikveh is written between a spring, which is totally natural, and a pit, which is filled totally by man. A Mikveh may not be totally Mayim She'uvim like a pit, nor must it be totally natural like a spring.

Rosh (Mikva'os 1): R. Tam says that it is a tradition from Sinai that three Lugim of She'uvim disqualify a Mikveh at the beginning. If three Lugim of She'uvim fall into an incomplete Mikveh, they disqualify it mid'Rabanan. He learns from R. Eliezer's law, that if the first Revi'is of water in a Mikveh was She'uvim, it disqualifies it. If three Lugim of Mayim She'uvim fall into an incomplete Mikveh, they disqualify it. Surely, he is more stringent about Mayim She'uvim at the beginning because it is mid'Oraisa!

Rejection (Rosh citing the Ri): No, R. Eliezer is more stringent about Mayim She'uvim at the beginning because it is a full Pasul Mikveh. A Revi'is is the Shi'ur Mikveh for Tevilas Kelim. We never find a tradition from Sinai about Mayim She'uvim. Even if we did, sometimes we say so about a mid'Rabanan law that is as clear as a tradition from Sinai.

Rashbam (66a DH u'Masmah, according to Rashash): Mid'Oraisa, a Mikveh must begin with (40 Sa'im of) water that is not She'uvim. If Mayim She'uvim falls in later, it is Batel. Yevamos 82b teaches that if a majority of She'uvim falls in, it disqualifies mid'Rabanan.

Tosfos (66a DH Michlal): The Rashbam and R. Tam say that if the entire Mikveh is Mayim She'uvim it is Pasul mid'Oraisa.

Source #1 (Toras Kohanim Shemini Parashah 9:1): Had it said 'Mikve Mayim Yihyeh Tahor', we would have thought that one may pour water to make a Mikveh. Therefore, it says "Mayan (u'Vor Mikve Mayim...)" to teach that a Mikveh must be like a spring, i.e. it is totally bi'Yedei Shamayim.

Rejection (Tosfos ibid.): Perhaps this is only an Asmachta.

Tosfos (ibid.): The Ri says that even if the entire Mikveh is Mayim She'uvim it is Pasul only mid'Rabanan.

Source #1 (Tosefta Mikva'os 2:1): If one left a Mikveh empty and later found it full, it is Kosher, for this is a Safek about Mayim She'uvim. Surely, we are lenient about the Safek because even all Mayim She'uvim is Pasul only mid'Rabanan!

Suggestion: Perhaps initially there was water inside that was not She'uvim.

Rejection: It does not say that the Mikveh was lacking, rather, that it was empty!

Rebuttal (and counter-proof - Rashba in Tosfos ibid.): The Tosefta says that the Mikveh is Kosher because the Chazakah is that Mikva'os are Kesherim, i.e. people make Mikva'os for Tevilah, so we may assume that it was not filled with She'uvim. If all Mayim She'uvim was Pasul mid'Rabanan, we would be lenient even without the Chazakah!

Support #1 (Seifa of the Tosefta): If there is a Keli near where water flows from a pipe (which is not a Keli) into a Mikveh, and we are unsure whether the water went directly from the pipe or if it went through the Keli, the Mikveh is Pasul, for the Pesul (the Keli) is evident. If the majority was Kosher water, the Mikveh is Kosher.

Rashba: We are stringent when it is possible that the majority was She'uvim for this is Pasul mid'Oraisa!

Support #2 (Tosefta Mikva'os 2:5): If there were two Mikva'os, one Kosher and one of She'uvim, and one does not know in which he was Tovel from Tum'ah mid'Oraisa and he touched Taharos, they are Safek Temei'im.

Rashba: We are stringent because it is a Safek mid'Oraisa!

Source #2 (for Ri - Pesachim 17b): Liquids (water) of Beis Mitbechai (the place where Korbanos are rinsed) in Kelim are Temei'im. If they are in the ground, they are Tehorim. In the ground is Tahor only if there is a Revi'is, for [mid'Oraisa] it is a valid Mikveh to be Tovel small Kelim.

The Gemara is Metaher even Mayim She'uvim, for it contrasts water in the ground to water in Kelim. Also, Stam liquids of Beis Mitbechai are She'uvim.

Rejection #1 (Rashba in Tosfos ibid.): Indeed, the Tosefta discusses only liquids that are now in the ground; it is Metamei if they were once in Kelim, and is Metaher if they were never in Kelim.

Rejection #2 (R. Moshe of Pontiza in Tosfos ibid.): Even though Mayim She'uvim disqualifies a Mikveh mid'Oraisa, water in the ground is Tahor because this was through Hamshachah, i.e. when water falls on level ground it spreads out. A Mikveh made totally from Mayim She'uvim via Hamshachah is Kosher mid'Oraisa.

Question: Only the minority may be from Mayim She'uvim via Hamshachah (Temurah 12a)!

Answer: That is mid'Rabanan.

Question: If a Mikveh of all Mayim She'uvim is Pasul mid'Oraisa, we understand why three Lugim are Posel mid'Rabanan. People used to Tovel in stinking water in caves. Afterwards, they would pour three Lugim of She'uvim on their heads. People used to say that the Mikveh is not Metaher, only the Mayim She'uvim are (Shabbos 14a), so Chachamim decreed that three Lugim are Posel. However, if all She'uvim is Kosher mid'Oraisa, why is there any decree about Mayim She'uvim?

Answer: It is a decree lest people immerse in a Keli. The Torah requires a Mikveh resembling a spring, i.e. in the ground.

Poskim

Shulchan Aruch (YD 201:3): The 40 Sa'im of a Mikveh may not be She'uvim. If they are, it is Pasul.

Rema: If the entire Mikveh is She'uvim it is Pasul mid'Oraisa. We must be stringent about a Safek. If the majority is Kosher and a minority is She'uvim, it is Pasul mid'Rabanan, so we are lenient about a Safek.

Beis Yosef (DH veha'Ran): The Ra'avad holds that She'uvim is Pasul mid'Oraisa if one poured the water in. If by itself the water came from the Kelim to the Mikveh, it is Pasul mid'Rabanan. R. Shimshon holds that She'uvim in a Keli that is Mekabel Tum'ah is Pasul mid'Oraisa. If the Keli is not Mekabel Tum'ah, e.g. it is of stone, the Mikveh is Pasul mid'Rabanan.