Final answer:
Acetylcholine is destroyed shortly after its release into the synaptic cleft through enzymatic degradation by acetylcholinesterase (AChE).
Step-by-step explanation:
The process that destroys acetylcholine a brief period after its release by the axonal endings is enzymatic degradation. This degradation is carried out by the enzyme known as acetylcholinesterase (AChE), which breaks down acetylcholine in the synaptic cleft, ensuring that the neurotransmitter cannot rebind to the postsynaptic receptors. This is crucial for terminating the signal, allowing the postsynaptic neuron to reset and be ready for the next wave of neurotransmission. Drugs that inhibit AChE, such as those used to treat Alzheimer's disease, can increase neurotransmission at synapses that release acetylcholine by preventing its breakdown and removal.