“Make like a banana and split” means “to leave” (“split” the scene) and is a pun on “banana split.” The saying has been recorded in teen slang since at least August 1972 and is similar to other humorous expressions, such as “make like a tree and leave.”
 
   
Wiktionary: make like a banana and split
Etymology
A pun on banana split and split (“to depart”)
Verb
to make like a banana and split
1. (idiomatic, humorous) to leave, depart
     
Google Books
Current Slang
University of South Dakota, Department of English
Volumes 2-5
1967 (The Google Books date is most probably not accurate—ed.)
Pg. 34:
Make like a banana and split, v. to leave.
—I’d better make like a banana, and split.
 
Google News Archive
29 August 1972, The Daily Sentinel (Middleport-Pomeroy, OH), “Generation Rap” by Helen and Sue Bottel, pg. 6, col. 1:
Instead of saying “Make like a nut and bolt,” or “Make like a tree and leave,” I will now make like a banana and split.—M.M.G.
 
One Potato, Two Potato…:
The Secret Education of American Children
By Mary and Herbert Knapp
New York, NY: W. W. Norton & Co., Inc.
1976
Pg. 64:
Be like a banana and split.
Be like dandruff and flake off.
Be like a tree and leave.
Be like a ghost and vanish.
Be like a bee and buzz off.
   
Google Books
Folklore for the Time of Your Life
By Elaine S. Katz
Birmingham, AL: Oxmoor House
1978
Pg. 28:
And did you reply, “Boss spelled backwards is double-s-o-b”? or “When they passed out brains, you thought they said trains and said, ‘I’ll wait for the next one’”? or “Why don’t you make like a tree and leave”? or “Make like a banana and split”?
   
Google Books
The Official Mork & Mindy Scrapbook
By Steven Seabrook
New York, NY: Pocket Books
1979
Pg. ?:
“Well, guess I’ll make like a banana and split.”
 
Google Books
I Scream, You Scream:
A Feast of Food Rhymes
By Lillian Morrison and Nancy Dunaway (illustrations)
Little Rock, AR: August House LittleFolk
1997
Back cover:
Be like a banana and split.