بسم الله الرحمن الرحيم
Cats sometime urinate or stool on clean floor and bed, it does not seem correct to think that it is due to mating, so there is no need to castrate it. Since castration of sheep and goat is done in order to make the meat soft. You should put the cat in some bag and leave it in some far off places, thus you will be safe from its dirt and also will be free from the headache of cleanliness.
Allah knows Best!
Darul Uloom Deoband
This answer was collected from the official ifta website of Darul Uloom Deoband in India.