Tosfos asks why doesn't this also teach us that women are obligated to wear Tzitzis just like they're obligated not to wear Shatnez. There is a similar Drasha in Erichin that wants to say for this reason Kohanim should be exempt from Tzitzis since they can wear Shatnez. (However, the Gemara ends up saying that Kohanim are obligated in Tzitzis since they are obligated not to wear Shatnez while they're not doing the Avodah.)
Tosfos answers that we learn that women are exempt from Mitzvos Aseh that are time related from a Hekish of all Mitzvos toT'filin. Just like woman exempt from T'filin which is time related so too all Mitzvos that are time related. A Hekish of P'sukim next to each other is stronger than Smuchim, Parshos written together. Therefore the Drasha to exempt wins out the Drasha to obligate.
However, Tosfos asks, if so then women should be able to wear Shatnez since they're not obligated in Tzitzis?
Tosfos answers that there must be some (unknown to us) Drasha to obligate women not to wear Shatnez.