c. 1300, "evil condition, misfortune, need, want," from Old French meschief "misfortune, harm, trouble; annoyance, vexation" (12c., Modern French méchef), verbal noun from meschever "come or bring to grief, be unfortunate" (opposite of achieve), from mes- "badly" (see mis- (2)) + chever "happen, come to a head," from Vulgar Latin *capare "head," from Latin caput "head" (from PIE root *kaput- "head"). Meaning "harm or evil considered as the work of some agent or due to some cause" is from late 15c. Sense of "playful malice" first recorded 1784.
Mischief Night in 19c. England was the eve of May Day and of Nov. 5, both major holidays, and perhaps the original point was pilfering for the next day's celebration and bonfire; but in Yorkshire, Scotland, and Ireland the night was Halloween. The useful Middle English verb mischieve (early 14c.) has, for some reason, fallen from currency.