After 7 children, my wife does not want to take birth control and we don’t want any more kids. Is a male vasectomy permissible halachically?
My apologies that it took some time to get back to you.
Please do not do this! To make things clear, a male vasectomy is biblically forbidden. In fact not only are we commanded not to make a human sterile, but we also not allowed to castrate an animal (dogs, cats). And just to being out he severity by which the Torah views this, a person that undergoes such an operation, may have serous issues marrying a regular Jew, as there is a biblical prohibition to marry a person who has been sterilized in this way.
There are a number of methods of birth control nowadays, and I would advise that you speak with your Rabbi and doctor, so that they can advise you better.
See Shulchan Aruch Even Haezer 5 paragraphs 1, 2, 8, and 11.