Cutting off circulation to the testicles fully or partially by tight binding of the scrotum above the testicles is more commonly known as banding, a form of castration play. Many men enjoy banding because it dramatically exaggerates sexual sensations and can provide more of a "rush" than a "normal" orgasm. In addition, the compression of the nerves dulls pain, and many men combine banding with heavy ball torture.
It is very important to note that tight binding even as short as an hour can in some cases result in permanent and irreversible damage, sometimes resulting in full castration. Please be careful if you enjoy this type of play unless you want to be a eunuch! It is essential that you be able to release the bands; do not underestimate how difficult it can be to remove industrial ties or even elastrator bands.
Banding cuts off circulation to the testes via the testicular artery. The artery runs alongside the ductus deferens and is therefore very superficial. Thus, constriction is likely to result in full occlusion of the testicular artery. This will result in anoxia (or the starvation of oxygen) and thus death of the testes, rendering the individual infertile.
Some men also enjoy banding the penis itself (which is far more resilient to damage, but certainly not immune either).