I was wondering if it is halachically forbidden to spay or neuter a pet (specifically a cat)?

Neutering a male animal is a Torah prohibition. In the case of a female there is a minority opinion that it is a Torah prohibition and a majority opinion that it is a Rabbinic prohibition. Generally, in regards to a female, many Poskim allow spaying by a non Jewish vet in a case of severe need. What constitutes great need is itself a question, some allow it in the case of house pets, others do not. In the case of males it is more complicated. For more info see an excellent article at: http://www.daat.ac.il/daat/english/halacha/jachter_1.htm In any case, a Rabbi should be consulted about the specific case.