When one spouse does not wish to practice birth control, but the other insists upon it, the Church allows the non-practicing spouse to engage in relations with the contracepting spouse for the sake of maintaining the marriage. The non-practicing partner is not allowed to use birth control himself, he must make his opposition to birth control known, and – at appropriate times – he should seek to educate his spouse about the morality of the practice. But, he can tolerate the fact that a contracepting spouse insists on birth control. In this case, you cannot agree to have a vasectomy, but you can engage in relations with your wife even if she insists on using birth control herself.
Frankly, I think you have larger issues here than birth control that you would do well to consider taking to a Catholic marital counselor: Your wife not only does not respect you (as demonstrated by your account of her emotional and verbal abuse of you), but she insists that *you *must be the one to permanently sterilize yourself (and thus mutilate your body) on threat of divorce. These are serious issues that should be addressed as soon as possible. I recommend contacting the Pastoral Solutions Institute or CatholicTherapists.com for a referral to a Catholic marital counselor in your area. If your wife refuses to seek therapy with you, I urge you to consider going by yourself. God bless.
Vademecum for Confessors Concerning Some Aspects of the Morality of Conjugal Life by the Pontifical Council for the Family