What is the punishment of a Muslim disgracing other Muslims?

Nothing can be done apart from warning him/her and giving good advice to that person. Religion is the main field of test. Discussions should be made to find the right way and such discussions are not in the scope of penal law. Difficulties caused by such behavior should be endured. The Glorified Allah commands:

“You will surely be put to test in respect of your properties and lives. And you will surely hear from those who were given the Scripture before you and from those who associate others with Allah much abuse. But if you be patient and guard yourselves – those are indeed the matters of determination.” (Al-e-Imran/ Family of Imran 3:186)

Being patient and cautious is the only way shown against disgracing words. The Messenger of Allah has suffered much from the hypocrites who converted to Islam and then returned; but he did not punish them in any ways. The Surah Al-Munafiqun is important from this aspect. You should read and heed on that Surah.