All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
In general, it is permissible to kill the harmful cat, as has been stated by the scholars of Fiqh, provided that it is believed that its harm will be repeated.
Al-Hattaab, from the Maaliki school of Fiqh, said in Mawaahib Al-Jaleel:
“Al-'Izz ibn 'Abd as-Salaam was asked about killing the harmful cat, is it permissible or not. He replied, 'If its harm is beyond the usual harm of cats, and its harm is repeated, then it becomes permissible to kill it. Regarding the first reason (if its harm is beyond the usual harm of cats): if what it does is its usual nature, such as eating meat if the cat is left alone with it, or if there is a cover on the meat which the cat can lift, so if the cat lifted it and ate from the meat, it is not to be killed, even if this act is repeated by it, because this is its nature. Regarding the second reason (if its harm is repeated): then as long as the cat did that harm by accident, it should not be killed; as in this case, it is not like a person or an animal that is not expected to change.'”
Allaah knows best.