We found one dictionary that defines the word cut one's stick:

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1. cut one's stick: Wiktionary

Definitions from Wiktionary (cut one's stick) ▸ verb:  (colloquial, intransitive) To depart. ▸ Words similar to cut one's stick ▸ Usage examples for cut one's stick ▸ Idioms related to cut one's stick ▸ Wikipedia articles (New!) ▸ Words that often appear near cut one's stick ▸ Rhymes of cut one's stick ▸ Invented words related to cut one's stick