Shmuel says that anyone who fasts is called a sinner for abstaining from the worldly pleasures that he is entitled to. The gemara draws a parallel between the statement of Shmuel regarding fasting and the statement of R. Elazar HaKafar who says that a Nazir is called a sinner for abstaining from wine. R. Elazar disagrees with R. Elazar Hakafar and holds that a Nazir is called a kadosh. The gemara assumes that just as R. Elazar says that a Nazir is a kadosh, one who fasts should also be a kadosh, and therefore asks from a statement of R. Elazar himself which implies that it is forbidden to fast. The gemra concludes that as long is someone is able to withstand the fast they are called a kadosh, as is the Nazir, but if one cannot withstand it and accepts it, it is improper (persumably because they are putting themself in a situation where they are likely not to complete the fast).
Tosafos asks that the gemara in Baba Kama implies that according to Shmuel one who fasts is not called a sinner, so how does Shmuel himself consider him a sinner? Tosafos answers that based on the kal v'chomer from Nazir who R. Elazar Hakafar considers a sinner, there is no question that one who fasts is certainly a sinner. But, Shmuel admits that the mitzvah which is accomplished through the fasting overwhelms the aveira aspect of it. Tosafos compares this with one who fasts a Ta'anis for a dream on Shabbos where the benefit offsets the loss, but there is still an aspect of aveira for which the need to do teshuva - ליתיב תענית לתעניתיה. The Gevuros Ari asks that he doesn't understand the category of an action having an aspect of Mitzvah and an aspect of Aveirah at the same time. Just as when we have an aseh pushing off a lo ta'aseh, we don't consider it to be an aveira at all because the Torah wants the mitzvah to be done at the expense of the aveira; similarly here we should consider it a pure mitzvah since the mitzvah will fully compensate for offsetting the aveira?
Before we answer the question of the Gevuros Ari, we need to understand whether Tosafos applies only to Ta'anis or even to a Nazir. When R. Elazar HaKafar says that a Nazir is a sinner, will the mitzvah aspect of being a Nazir be mixed with aveirah so that there is both? From Tosafos it seems that we only consider Ta'anis to be this hybrid of mitzvah and aveirah, but Nazir is a pure aveirah. Perhaps Tosafos is assuming like the Rashash explains that R. Elazar HaKafar is only addressing a Nazir Tamei (which is the pasuk that he quotes). For the days that preceeded his tu'mah there is an aveirah without any mitzvah because those days didn't ultimately count toward nezirus. However, for a Nazir Tahor perhaps we would consider the mitzvah to completley outweigh and over compensate for the aveira so that it is not considered an aveira at all. According to this approach, by Nazir there is no middle category of partial mitzvah, partial aveirah, where the mitzvah is bigger than the aveirah. By a Nazir Tamei it is considered a pure aveira and by a Nazir Tahor it is considered a pure mitzvah (similar to aseh docheh lo ta'aseh as the gevuros ari is suggesting). However, the Maharsha (agados) points out that Tosafos in Baba Kama seems to hold that even a Nazir Tamei according to R. Elazar HaKafar would be in this middle category where there is a hybrid of mitzvah and aveirah, just that the mitzvah is greater.
Lets return to the question of the Gevuros Ari regarding the hybrid category, and not considering the mitzvah to over compensate to the aveira to the point where the aveira virtually doesn't exist. It is true that by aseh docheh lo ta'aseh we consider the mitzvah to overcompensate for the aveira to the point where we do not consider there to be any aspect of aveira at all. However, this is only because we have a gezeiras hakasuv that we learn from Tzitzis teaching us עשה דוחה לא תעשה. To me it seems that it is more comparable to a case where we allow a greater aseh to take precendence over a lesser aseh. For example, the gemara says in Pesachim that the mitzvah of Pesach for which there is kareis overrides the mitzvah of making the Tamid shel bein ha'arbayim the last korban of the day. Perhaps in that case the lesser aseh is still considered violated and one would indeed require some amount of teshuva for that.