It does its work after the neurotransmitters enter the synapse. Think of neurotransmitters as being like letters mailed through the post office. If you were trying to send a letter to a friend, a pre-synaptic neurotoxin would stop you from mailing the letter. A post-synaptic neurotoxin would jam up your friend's mailbox so that the mail could not go in. Either way, your friend would not get the letter.
Neurotoxins are just one kind of poison found in snake venom.
Different snakes carry different kinds of toxins. Some venoms, called myotoxins, damage muscle cells. Others interfere with the blood clotting process. Still others actually promote clotting. In addition, a single venom can have different effects on different types of cells.