Green’s Dictionary of Slang

jump off v.

1. to begin, e.g. of a military attack.

[US]Parkman in Knickerbocker (N.Y.) XXIX 316: It was resolved to remain one day at Fort Leavenworth, and on the next to bid a final adieu to the frontier; or in the phraseology of the region, to ‘jump off’ [DA].
[US](con. 1944) N. Mailer Naked and Dead 655: We’re going to be ready to jump off in fifteen minutes.
[US](con. 1950) E. Frankel Band of Brothers 69: We jump off at 0600.

2. (US) to leave.

[US]A.H. Lewis Wolfville 18: He saddles up a pinto pony [...] an’ jumps off every now an’ then for two an’ three days at a clatter.
[Aus]Gippsland Times (Vic.) 1 Oct. 4/1: Good-bye Mo, you’re through / [...] / You’re at the jump-off station / So Moham adieu.

3. to happen, to start happening.

[US]C. Himes ‘His Last Day’ in Coll. Stories (1990) 297: I was home and in bed when that killing jumped off.
Son House in S. Calt Rather Be Devil (1994) 96: Get half drunk off that white lighning whiskey, [...] anything was liable to jump off .
[US](con. 1960s) D. Goines Black Gangster (1991) 34: When all that burning and looting jumped off in ’67.
[US]Ice-T ‘Six in the Morning’ [lyrics] Deuced it to the Bronx to rest our heads / Where a shoot out jumped off nine people lay dead.
[US]N. McCall Makes Me Wanna Holler (1995) 57: I’d risk missing lunch and dinner waiting for some action to jump off.
[US]J. Lerner You Got Nothing Coming 50: They try to pull this lock-down shit in Kansas and the shit would’ve jumped off big-time.
[US]R. Price Lush Life 36: [...] and not to get too smashed in case something did actually jump off .
[US]G. Hayward Corruption Officer [ebk] cap. 13: The ratio of inmate to Officer was on the inmate side when things first jumped off.

4. of a person, to start doing something.

[US]E. Torres After Hours 31: I’m waitin’ for one of them to jump off.

In phrases

jump off the porch (v.)

(US black) to start a career selling drugs.

Jeezy ‘Bout That’ [lyrics] Jumped off the porch but I landed on my feet / [...] / Jumped off the porch at eleven, bitch I been bout it.