Is It Permissible to Euthanize or Neuter Your Pets?
In the name of God, the Most Gracious, the Most Merciful.
It would not be permissible to have the cat killed even though it is in agony. It is a living soul and its death should not be effected by its owner. It should be allowed to die its natural death. However, if the animal is close to dying and there is no chance of recovery it could be slaughtered to relieve the pain. [Radd al-Muhtar 5:305]
It is permissible to castrate animals if some benefit is derived thereof, for example the animal becomes more healthy or its meat tastes better, etc. or it can save from some harm. In the case in question if there is nowhere to send the kittens and they are becoming a nuisance around the hose or locality then it would be permissible to spay it. [Fatawa Hindiyya 5:357]
And Allah knows best.
Answered By: Shaykh Mufti Muhammad ibn Adam al-Kawthari