All praise is for Allaah alone, and may he send peace and blessings upon His Messenger, His Messenger's family, and His Messenger's Companions.
It is not allowed to make fun of a person who grows his beard, because growing it is only obedience to the order of Allaah's Messenger Salallaahu alayhi wasallam. You should advise the mocker, explaining to him that by making fun of the beard, he may not only be committing a major sin but he also may be committing an act of apostasy. Allaah Almighty says:
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Say: "Was it at Allâh, and His Ayât (proofs, evidences, verses, lessons, signs, revelations, etc.) and His Messenger Salallaahu alayhi wasallam that you were mocking?"
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Make no excuse; you have disbelieved after you had believed [At-Taubah 9:65-66]
And Allaah is the Granter of Success. May Allaah send peace and blessings upon our Prophet Muhammad, his family, and his Companions.