Green’s Dictionary of Slang

1. to leave, to depart from a place.

1904		Number 1500 Life In Sing Sing 261: I blew out and rung in with a couple of penny-weighters. A Tommy and his papa.
1910		Bulletin (Sydney) 29 Sept. 10/4: One afternoon a lady floated in and threw a smile. The man – a Scotsman – bounded up, hugged the lady three times, reached his hat and blew out. He never came back.
1923		H.C. Witwer Fighting Blood 246: I blowed out of the office, fit to be tied.
1932		(con. 1910s) J.T. Farrell Young Lonigan in Studs Lonigan (1936) 147: He blew out, [...] went on the bum like a damn fool.
1972		J.B. Keane Letters of Irish Parish Priest 63: If I hear as much as another word out of you or the bloody bishop I’ll blow the hell out of here to England.
2010		C. Hiaasen Star Island (2011) 28: I’ll probably blow out of here tomorrow.

2. to send away, to reject.

1905		Eve. Star (Wash., DC) 28 May 39/2: I’ll give you just one minute to get out, or I’ll blow you out!
1986		S. King It (1987) 478: They had a public City Council meeting about it, and Hanlon blew those suckers out.