As a joke, perhaps. Otherwise, no. The meaning of "speechless" (as you can confirm in your favourite dictionary) is "temporarily unable to speak, due to shock, surprise etc."
Mute tends to mean "unable to make a sound". I'd just say "It can't talk" or in this context "It can't tell you to stop." etc. It isn't common, since talking cats are the exception, not the rule. You don't usually need to make a point about it.
Voiceless is more often used figuratively, meaning "not able to express an opinion" and applied to humans. A cat does have a voice, it goes "miaow miaow".
In the past "dumb" was used in this context, but now that has picked up the meaning of "stupid" in this kind of casual language, so I don't recommend it (the fixed expression "dumb animal" is possible, but not "dumb cat").