J.E. Lighter, The Random House Historical Dictionary of American Slang (1994) notes that expression also appears in the closely related forms "blow this pop stand" and "blow this popcorn stand." Lighter includes this entry under blow:
c. trans[itive] to leave (a place or (rarely) a person); (in recent stu[dent] use) in phr[ases] of the type blow this pop stand leave this place.
[Earliest relevant citations;] 1974 Univ[ersity of] Tenn[essee] student: Let's blow this pop stand. 1980 Mork & Mindy (ABC-TV): How about you and me blow this Popsicle stand? 1983 Nat[ional] Lampoon (Feb.) 16: Let's blow this popcorn stand.
The earliest matches in a Google Books search for all three wordings are for "let's blow this pop stand." From Ann Arbor [Michigan] Huron High School, Full Circle (1969) [combined snippets]:
"Good heavens, what if someone were to see this mess!" With the coming of noon all the words slowly began to fuse together in Dunken's mind. "Man oh man, with melodic harmony I should gracefully be banished from the face of the earth to eat my pome. Well shoot me at dawn!"As a fellow junkmate put it, "Tap the rap, plop the top, and blow this pop stand."
Also, from Esquire Fortnightly, volume 92 (1979):
Oh for heaven's sake all right that's it I'm going to blow this pop stand I know I'm just a dumb ignorant media person but if you think for one minute that ... I respect your uh conviction but this has got to be a delusionary belief. The man in the moon. A delusionary belief.
And from Maureen Strange, Sparks (1981):
"I don't have the right credentials — I'm not a creep. How the hell did we get on this subject I hate? Let's blow this pop stand. Let's go celebrate my success as a famous artist."
The earliest Google Books match for the "popcorn" variant is the National Lampoon article (February 1983) that Lighter mentions above.
The earliest Google Books match for the "Popsicle" wording is also from 1983— from David Bischoff, Wargames (1983) [combined snippets):
...You know, the ones who always wear gym clothes and smell so bad.”
“Yeah, well I'm probably not a real rose right now myself.” He guided her to an exit. “C'mon, let's blow this Popsicle stand.”
“My car's the other way, David,” Jennifer said.
The next match is from a letter writer from Philadelphia (Pennsylvania) to columnist William Safire, in William Safire, Take My Word for It (1986):
I was surprised to see no mention of the phrase "Let's blow this pop stand " Surely, this is a shortened version of the longer farewell "Let's blow this popsicle stand."
The common theme here is that soda-pop stands, popcorn stands, and Popsicle stands are chump-change operations. Prior to this round of enterprises, according to Lighter, common phrases suggested blowing "this joint," "this burg," "this place," "town," and "this scene." Lighter's first match for "blow this joint" goes back to 1902 in Billy Burgundy's Letters:
Now, old man, you know me, if there is anything on earth that will make me cough up freely it is a fairy that I am stuck on. I eliminated the $16; then we had another and blew the joint.
On our way up Broadway she stopped in to get a waist from the cleaner's. Knowing that she was shy, I produced the necessary three plunks salvage. Then I put her on a trolley and ducked into an emporium to lubricate my proud tonsils.
Earlier still (and the first of Lighter's citations for blew in meaning 6(c) is this one from William Kountz, Billy Baxter's Letters (1899):
In the general bustle (of a melee) a seedy looking man pinched the Fresh Air Fund, box and all. You know I'm not much for the bat cave, and to avoid such after-complications as patrol wagons and things, I blew the bunch and started up street. I guess the wind must have been against me, as I was tacking.
"Let's blow this pop/popcorn/Popsicle stand" is a relatively recent updating of an old slang expression from the turn of the twentieth century that blew "the bunch" or "the joint" instead of a stand.
Both Google Books (which finds a first match from 1969) and J.E. Lighter (with a match from 1974) identify "Let's blow this pop stand" as the earliest of the pop-related versions of the idiom. The Popsicle version shows up in 1980 (on the Mork & Mindy TV show, according to Lighter) and in 1983 (in David Bischoff's Wargames, according to Google Books).