The Gemara says that someone who has a pikadon is patur from answering the door to give tzedaka because he's osek b'mitzvah. How far does this go? How much does the pikdon have to be worth? Is he patur from putting on tefillin or davening. Is he not supposed to learn Torah? How long does this continue for?
Below are the Insights that we wrote for this Daf which address your question.
2) ONE WHO IS PERFORMING A MITZVAH IS EXEMPT FROM OTHER MITZVOS
QUESTION: RASHI (DH v'Hacha b'Shomer) explains that one who is watching an Aveidah is exempt from giving Tzedakah because of the principle of "ha'Osek ba'Mitzvah Patur Min ha'Mitzvah" -- "One who is involved in one Mitzvah is exempt from another Mitzvah." Hence, in the case of our Gemara, the person who is involved in the Mitzvah of Hashavas Aveidah is exempt from the Mitzvah of Tzedakah.
TOSFOS (Sukah 25a, DH Sheluchei Mitzvah) asks that according to this, one who is wearing Tzitzis or Tefilin should be exempt from all other Mitzvos!
(a) TOSFOS answers that only when the second Mitzvah would interrupt one's performance of the first Mitzvah, is the person exempt from the second Mitzvah. If one could perform the second Mitzvah without affecting his performance of the first Mitzvah (such as is the case when wearing Tzitzis or Tefilin), he is not exempt from the second Mitzvah.
The OR ZARU'A questions this answer of Tosfos. It is obvious that one may not stop performing one Mitzvah in order to perform another. Why would we have thought to give precedence to one Mitzvah over another, had the verse not taught us otherwise?
We could answer that Tosfos learns from the verse that one who is involved in one Mitzvah is exempt from other Mitzvos even in a case where the opportunity for the second Mitzvah will pass if it is not done right away. One might have thought that in such a situation, one should halt the performance of the first Mitzvah and fulfill the second Mitzvah. The verse teaches us that even in such a case, one may not leave the first Mitzvah to perform the second. (M. Kornfeld)
(b) RASHBA in the name of RAV HAI GA'ON, the MAGID MISHNAH (Hilchos Sukah 6:4) in the name of the GE'ONIM, and the OR ZARU'A (Hilchos Sukah) explain that as long as a person is involved in preparing to fulfill a Mitzvah, such as when he is traveling in order to perform a Mitzvah, he is not obligated by the Torah to perform other Mitzvos even if they do not distract him from the first Mitzvah. The Almighty does not give us two things to do at one time.
With regard to Tzitzis and Tefilin, however, one has already done what was needed to fulfill the Mitzvah. He is now in the process of fulfilling the Mitzvah, and not in the process of preparing to fulfill the Mitzvah. The exemption from other Mitzvos applies only when one has not yet fulfilled the first Mitzvah, and is doing something in order to fulfill the Mitzvah.
(c) The RAN (Sukah 25a) makes a compromise. He agrees with the Rashba that one is exempt from the second Mitzvah even if performing it does not distract him from the first Mitzvah. However, if there is a way to fulfill the second Mitzvah while still performing the first Mitzvah in its normal manner , then one is not exempt from the second Mitzvah (as the Ran writes, "Why not fulfill a Mitzvah if nothing is lost in the process?"). Only when one must change his normal way of performing the first Mitzvah in order to fulfill the second Mitzvah is he exempt from the second Mitzvah.
(It could be that according to the Ran, the obligation to do the second Mitzvah does not stem from the normal obligation to perform Mitzvos, but rather from the requirement not to disgrace a Mitzvah. Technically, he may be exempt since he is involved in another Mitzvah. But in practice, since the second Mitzvah could be performed without making any change from one's normal way of performing the first Mitzvah, it would be disgraceful to the second Mitzvah not to perform it. -M. Kornfeld)
HALACHAH: The REMA (Orach Chayim 38:8) cites the opinion of the Ran as the Halachah; when there is a way to fulfill the second Mitzvah while still performing the first Mitzvah in its normal manner, then one is not exempt from the second Mitzvah. Otherwise, he is exempt.