Correct spelling, explanation: this form is correct; its origin goes way back to the Anglo-French appointer. This origin is where double p comes from (point and prefix a-). Then, the prefix dis- was added. Therefore disappoint is the correct form, and disapoint is incorrect.

Definition of disappoint:
verb, to fail to meet the expectations
Every time you say you couldn’t do this, you disappoint me.
Please do not disappoint me and be on time.

Incorrect spelling, explanation: since Anglo-French origin appointer has got double p, this spelling remained. In the word disappoint, which is further meaning, but from this root, it is present as well. Therefore disapoint is incorrect. Double p probably arose when prefix a- was added to word point, hence disappoint is correct.

Incorrect spelling