The sentence is wrong. There are two possible ways of saying this. Note the plural 'women':
Feminism is not a stick with which to beat other women.
Feminism is not a stick to beat other women with.
The speaker should not have put the extra 'with' at the end of the sentence. This is a clear case of someone mispeaking. It's actually very common in natural, unrehearsed conversations to make slips of the tongue of this type.