The first Mishna in Massekhet Ḥullin teaches that this mitzva can be performed by anyone, excluding people who are viewed as incompetent, like a ḥeresh (a deaf-mute, who was considered to be uneducatable in the time of the Mishna), shoteh (an “imbecile”) and a minor, who has not yet reached the age of maturity.
Tosafot point out that from the Mishna it appears that women are included among those who are acceptable as ritual slaughterers, and the fact that the Mishna 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 mitzva. Nevertheless, the rishonim quote sources (variously Hilkhot, or Hilkhot Eldad HaDani), which preclude them from acting as shoḥatim because nashim da’atan kalot – that halakha perceives women as being “lightheaded.” Those works includes a number of other restrictions in the act of sheḥita; for example, sheḥita 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 ḥumrot – 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 Massekhet Zevaḥim (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.