I guess technically semen is neither vegan or vegetarian, since it is an animal product, but semen technically is not alive either. Life does not start until semen fertilizes an egg. (im not trying to make a political statement here because it i know it sounds like it)
Interesting too are viruses, they are not alive until they have infected a cell. Red blood cells also are not alive, but a product of animals, unlike brain cells which are living cells. semen is basically encapsulated genetic material that requires items from an female egg to produce a life form.