"Mi gato se casó, será papá" would be correct Spanish, however, the "se" is called a reflexive pronoun in grammar, and I am no grammar professor. It is enough to say that it cannot be defined by itself, you have to know how it is used, because it is just a "helper" for verbs.

In this case it could be illustrated as "himself", such as "My cat got himself married", because to leave it out would indicate someone who marries other couples by performing the ceremony, such as a priest, minister, judge, etc.

Start studying Spanish and you'll find it fascinating. And as far as cats are concerned, like some men, they don't even stick around 5 minutes more after the deed is done. They're "outta there".