I have been using slept off to mean that I fell asleep. For example,
I slept off early yesterday.
Is that used correctly?
You are confusing two common English expressions:
I went to bed at 11pm, and soon dropped off (to sleep).
He had had too much to drink at the party; he had to take a taxi to his London flat, where he slept off the effects of the claret and whisky.
You need 'drop(ped) off'.