Vasectomy for the purpose of birth control is not morally acceptable. The
Catechism of the Catholic Church (CCC) teaches, “every action which, whether in anticipation of the conjugal act, or in its accomplishment, or in the development of its natural consequences, proposes, whether as an end or as a means, to render procreation impossible is intrinsically evil” (CCC 2370).
Pope Paul VI specifically addressed vasectomy (and tubal ligation) in his encyclical
Humanae Vitae (HV) when he stated, “to be condemned, as the magisterium of the Church has affirmed on many occasions, is direct sterilization, whether of the man or of the woman, whether permanent or temporary” (HV 14).
You may, however, wish to consider Natural Family Planning (NFP). For more on this see
The Couple to Couple League.
Suggested reading:
Do I have to have a large family?
What are acceptable reasons for avoiding pregnancy?