The blood supply to each testicle is redundant and numerous. Theoretically, if a significant portion of the blood flow to the testicle has been interrupted then the testicle could suffer enough damage to become atrophic (smaller). In severe cases this could result in complete loss of function to the effected testicle.
Although impaired testicular blood flow is a possible risk of vasectomy, it is a very rare complication and is estimated to happen in about 1 out of every 10,000 vasectomy procedures or <0.01%.
A significant insult to the testicular blood flow would most likely require an uncommon and severe vasectomy complication in a patient with pre-existing vascular compromise.
The patient would also likely have a pre-existing vascular insufficiency or have a preexisting vascular insult (previous hernia surgery, pelvic surgery, diabetes or other medical conditions which can cause vascular disease) that would exponentially exacerbate the vasectomy insult to the testicle.
Although impaired testicular blood flow is possible, most men can seek vasectomy with the reassurance this is a very unlikely complication.