Sperm are made in the testicles. At the time of ejaculation, the sperm travel from the testicles and a structure called the epididymis through the vas deferens and then out through the ejaculatory ducts and finally out through the penis and urethra. When sperm are propelled through the ejaculatory ducts, they are joined by fluid made by the prostate and seminal vesicles. The testicles make all the sperm, but the prostate and seminal vesicles make 95% of the fluid.
What vasectomy does is to block the sperm from getting out of the testes and epididymis by dividing and occluding vas deferens. A small piece of the vas is also commonly removed ('vasectomy"). Since most of the fluid in the ejaculate is made in the seminal vesicles and prostate, even after vasectomy a normal amount of fluid will come out but it will not contain any sperm.