Is it permissible to put down your cat if it’s suffering from tumor?

Bismillahi Ta’ala

Walaikum Assalam Warahmatullah

Yes, it is permissible to humanely euthanize your cat when there is a need established as mentioned in your question.

Wallahu A’lam

And Allah Ta’āla Knows Best
Mufti Faisal al-Mahmudi