What is the difference between ‘I'm never having a beard when I grew up’’ and 'I will never have a beard when I grew up'?
Are the two sentences the same in meaning or they are different?
The two are very similar and could easily be interpreted to mean the same thing, but there are subtle differences in what the speaker might have meant:
With I'm never having the speaker might be resolving to never have a beard, because he really doesn't want one. (This is progressive tone; we hear the future lack of a beard as something the speaker will maintain by force of will.)
With I'll never have the speaker might have concluded that he (she?) is permanently unable to grow a beard, either physically (perhaps genetically, or perhaps a skin disease), or perhaps a rich aunt's will prohibits bearded relatives from inheriting. (This implies a pefective aspect; we hear the future lack of a beard as something out of the speaker's control).
It's a little farfetched in the specific case of beards: you really have to strain to think of a plausible situation for the "I'll never have" version.
But the difference is much easier to see between "I'm never having a Mercedes" (from an Audi lover) and "I'll never have a Mercedes" (sigh, I'll never be able to afford one).
These are the two different forms the Simple Future tense in English:
Be going to (written as "I'm never having", implied as "I am never going to" in your question), and
Will (written as "I will never" in your question)
The two can generally be used interchangeably, although they typically express subtly different meaning. For example, form #1 will be used more often to indicate something being done to the subject, while form #2 almost always indicates something the subject will him or herself do.
In many cases the "simple will" form (#2 above) is considered more direct and generally clearer language. The statement imparts more confidence and may therefore be the preferred choice in many cases.
One other note: something that makes your first phrase sound less articulate than the second is that you've used "having" instead of "going to have" (or even better..."going to grow"). For example, it would sound better to say "I am never going to grow a beard when I grow up."
In this case, given the way you're written both sentences, their meaning would be the same.