The TOSFEI HAROSH (Nidah 61b, DH "Shua") explains the argument between RASHI and RABEINU TAM in a clear fashion. Rashi holds that wool and linen must undergo Shua together , Tavi together, and Nuz together in order for it to be Shatnez. Rabeinu Tam holds that the process of Shua, Tavi, and Nuz must be done to both the wool and the linen, but they can be done separately. After these processes are done to both the wool and the linen, the combination of the two threads makes creates Shatnez.

According to Rabeinu Tam, Rav Ashi proceeds to ask how Mar Zutra knew that all of these processes had to be done to both the wool and linen in order to create Shatnez. Maybe the process of Shua alone, or Tavi alone, should be enough to produce Shatnez? The Gemara answers that as they are all alluded to in one word, the Pasuk implies that they must all be done to both the wool and linen in order to create a prohibition of Shatnez.

All the Best,

Yaakov Montrose