Anatomy of a vasectomy
Semen is the liquid that comes out from the penis during ejaculation. The vast majority of this liquid is produced just behind the penis in the prostate and seminal vesicles. Sperm are the tiny cells that cause a pregnancy. Sperm are produced in the testicles. From the testicles, sperm move into the collecting apparatus called the epididymis, and then from the epididymis up into the vas deferens. A vas deferens is a tube that carries sperm from the epididymis up to the prostate.
After a vasectomy, each of the vasa are divided. Notice in the diagram that the connections between the prostate, seminal vesicles, and penis are still intact. Thus, when you ejaculate, you still make the liquid semen. The only difference is that the semen will not contain the little sperm cells. Since sperm make up only about 3% of the semen, the volume is essentially unchanged.