Do vasectomies eliminate the production or buildup of semen so that they no longer require discharge as the male body does when functioning normally?

The major portion of the ejaculate is produced by the prostate gland. The sperm cells are produced in the testes along with a tiny amount of fluid to transport them to be combined with the prostate's contribution. A vasectomy severs the vas deferens, preventing the sperm from leaving the testes. The prostate continues to produce the normal amount of "cum".

Strictly speaking, a 1-5% reduction in volume is possible. In practice, this falls below the detection threshold under normal circumstances.