Student or Learner
"They haven't received it as of yet"
"They don't have it as of yet"
Are these correct?
Neither is correct because they don't end with a punctuation mark (come on, tufguy - are we still reminding you about this?)
Regarding the actual wording, no. "As of yet" is one of those phrases that elicits apoplexy in some native speakers - it's completely pointless and meaningless. Stick with "yet". You don't even need "as yet" in your context.
They haven't received it yet.
They don't have it yet.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.