c. 1300, "evil condition, misfortune; hardship, need, want; wickedness, wrongdoing, evil," 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" is recorded by 1784. The meaning has softened with time; in Middle English to be full of mischief was to be miserable; to make mischief was "to result in misery."
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.), used by Skelton and Gavin Douglas, has, for some reason, fallen from currency.