The first Mishnah in Masechet Hullin teaches that this mitzvah can be performed by anyone, excluding people who are viewed as incompetent, like a heresh (a deaf-mute, who was considered to be uneducatable in the time of the Mishnah),shoteh (an “imbecile”) and a minor, who has not yet reached the age of maturity.
Tosafot point out that from the Mishnah it appears that women are included among those who are acceptable as ritual slaughterers, and the fact that the Mishnah does not choose to emphasize that by stating clearly “both men and women” is because there is no reason to think that women would be excluded from this mitzvah. Nevertheless, the rishonim quote sources (variously Hilkhot, or Hilkhot Eldad ha-Dani), which preclude them from acting as shohatim because nashim da’atan kalot – that halakhah perceives women as being “lightheaded.” Those works includes a number of other restrictions in the act of shehitah; for example, shehitah performed by someone who was not properly dressed or someone who did not recite the appropriate benediction at the time of slaughter will be invalid.
Tosafot argue that in all of these cases, these are humrot – stringencies – established by the author of that work that are not actually requirements of Jewish law. With regard to women performing ritual slaughter, Tosafot point out that the statement in Masechet Zevahim (31b), which clearly states that women can act as ritual slaughterers in the Temple.
In any case, at least in the Ashkenazi world, we do not find that women served as ritual slaughterers for the community. And although they certainly were able to slaughter animals in the Temple, some suggest that the circumstances in the Temple were such that there was less concern for “lightheadedness” than there is in ordinary slaughter.