Couples are encouraged to have as many children as their financial situations allow. They do not encourage men to keep their wives barefoot and pregnant all their lives. The Roman Catholic Church allows for family planning, but when it comes to the use of artificial means of birth control like contraceptives, either barrier (condoms, IUD, etc.) or hormonal (birth control pills) it is against the rules. Likewise tubal ligations, hysterectomies and vasectomies for the purpose of sterilization or contraception are also out. However, if the procedures are due to a medical necessity then you truly can have a Catholic vasectomy.
If you are a devout Catholic and want to keep from getting pregnant here is what can you do. Natural Family Planning methods are taught by the Church as ways to reduce the risk of pregnancy without artificial means. Methods like basal body temperature charting, the rhythm method, or the Standard Days Method and periods of abstinence during the woman’s menstrual cycle are all natural ways to prevent and reduce the risk of pregnancy.
Having researched the question in many Catholic forums I have found that it is not possible to have a Catholic vasectomy. It would be a mortal sin and condemn you to damnation for all time if you had one. If you have had a vasectomy and come to the Catholic faith later you will need to confess your sin to the priest and if it would not force a considerable financial burden on you and your family you should investigate a vasectomy reversal procedure. If it will place a burden on the family you may be able to petition the Church for dispensation. The ideal of creating a world of fertility in the marriage bed is what the Catholic Church strives for. Sexual relations within the marriage vows are to be encouraged. As a good Roman Catholic do not entertain a vasectomy.