To be short-tempered is to be someone that gets easily angered. To snap at something means to quickly take an angry tone with someone. To snap can also mean to break suddenly. The word snap fits the vine in both ways. The vine is personified as being short-tempered, but it can also be physically snapped, or broken by the wind. This joke is a play on the word snap and its different meanings.
Vines are extremely short - tempered . They snap at the slightest wind .