The claim of Natural semantic metalanguage is that you can with around 60. It was a party trick of Australian linguistics undergrads to speak in NSM; it becomes very stilted very quickly, but in principle you can define a lot of notions with a limited vocabulary, as the asker alludes to. NSM is of course a definition language, rather than a communicative language, but that seems to be what OP is after.
Basic English tries with 850 words, and xkcd’s Up Goer Five English that Robert Collins mentions seems to be of the lineage of Basic English.