Clearly Islam does not support free speech.
You'll notice that no earthly punishment is mentioned for those who mock Islam. Promises of chastisement in the hereafter can hardly be considered suppression of free speech - mock as much as you'd like.
...Go on mocking, surely Allah will bring to light what you fear. - 9:64
Free speech in Islam as encouraged by the Caliph Ma'mun's cousin Hashimi:
... bring forward all the arguments you wish and say whatever you please and speak your mind freely. Now that you are safe and free to say whatever you please appoint some arbitrator who will impartially judge between us and lean only towards the truth and be free from the empery of passion, and that arbitrator shall be Reason, whereby God makes us responsible for our own rewards and punishments. Herein I have dealt justly with you and have given you full security and am ready to accept whatever decision Reason may give for me or against me. For "There is no compulsion in religion" (Qur'an 2:256) and I have only invited you to accept our faith willingly and of your own accord and have pointed out the hideousness of your present belief. Peace be with you and the blessings of God!