Spermicide - How does it kill sperm? Is sperm alive?

Is sperm even alive to be killed? How can a substance kill something that is not alive?

Sperm is most definitely alive. And spermacides work by poisoning it, more or less.

Sperm are living cells. Nonoxynol acts to break down a sperm’s acrosomal membranes; breakdown of membranes immobilizes the sperm. The nonoxynol plays the role of a surfactant.