In the picture above one can see the white epididymis transitioning into the vas deferens. Follow the blue arrow. You can see where the vas is cut (red), fulgurated (green) and tied (yellow).
The answer to the question: Two things happen.
There is a blockage after the vasectomy and this cause a mild back pressure. The vas dilates due to this and as a result there is a markedly decreased production of sperm.
The sperm in the vas is also broken down initially into sperm parts and over time eventually becomes a creamy fluid of amorphous debris.
At the time of a vasectomy reversal these changes are seen. A dilated vas on the testicle side of the vasectomy and visual and microscopic changes of the fluid which is released when the vasectomy site is incised.
Fun fact: Only approximately 5-10% of the ejaculate is sperm, the majority is from the prostate so there is very little noticeable change in the volume of the ejaculate after a vasectomy.