Blasphemy against Islam and the Prophet Muhammad is taken very seriously by many Muslims, apparently. Depending on the country, it is also possible that a person who blasphemes about Islam or the Prophet is going to be subject to some kind of punishment according to the laws of that country. The common reasoning for this is that anyone who mocks or insults the Prophet has become an apostate, and thus they should be killed. That in itself is a misunderstanding of the religion. There are also some hadiths (or sayings of the Prophet) that a Muslim may refer to in order to defend punishment for blasphemy, although those are still not conclusive evidence for punishment.
On the other side of the argument, there is no Quranic instruction that supports the aforementioned opinion. Rather, the Quran points to the opposite direction. In some verses God tells us that when we hear some evil or offensive speech, we should simply ignore them and walk away. We should avoid getting into arguments and instead just turn away from them peacefully as He says (referring to believers):
"And when they hear vain speech, they turn away from it and say, 'For us are our deeds, and for you are your deeds. Peace be upon you; we seek not the ignorant.'" (Surah 28:55)
"When you hear those who engage in vain discourse about Our signs, then turn away from them until they enter into another theme. And if Satan causes you to forget, then do not sit, after the remembrance, in the company of the wrong-doers." (Surah 6:42)
So the act of murdering 10 people just because they drew a cartoon of Muhammad is clearly not within the bounds of Islam.
There are also verses which mention how the disbelievers of that time used to mock and insult the Prophet Muhammad - and other Prophets as well - but once again, the Quran doesn't command us to carry out any physical punishments on them. It just tells us to leave them alone because their punishments will be brought to them soon enough ... "So leave them to plunge in vain talk and amusement until they encounter that Day of theirs which they have been promised" (Surah 70:42).
People used to say unspeakably cruel things to the Prophet Muhammad, but he never enjoined any punishment on those people. For years he was mocked, insulted, challenged, pushed out of Mecca, his companions were beaten, abused, and even killed, he was spit on, he was beaten so severely that there was blood dripping from his face, the Quraish rejoiced at the fact that all of his sons died so early, they boycotted his followers, and so on and so forth, and yet he was praying for guidance and forgiveness for the same people who were hurting him.
Here are some further logical answers that explain why the "blasphemy laws" that exist today are clearly contrary to Islam:
What is the Punishment for Blasphemy in Islam?
On the other side of the argument, there is no Quranic instruction that supports the aforementioned opinion. Rather, the Quran points to the opposite direction. In some verses God tells us that when we hear some evil or offensive speech, we should simply ignore them and walk away. We should avoid getting into arguments and instead just turn away from them peacefully as He says (referring to believers):
"And when they hear vain speech, they turn away from it and say, 'For us are our deeds, and for you are your deeds. Peace be upon you; we seek not the ignorant.'" (Surah 28:55)
"When you hear those who engage in vain discourse about Our signs, then turn away from them until they enter into another theme. And if Satan causes you to forget, then do not sit, after the remembrance, in the company of the wrong-doers." (Surah 6:42)
So the act of murdering 10 people just because they drew a cartoon of Muhammad is clearly not within the bounds of Islam.
There are also verses which mention how the disbelievers of that time used to mock and insult the Prophet Muhammad - and other Prophets as well - but once again, the Quran doesn't command us to carry out any physical punishments on them. It just tells us to leave them alone because their punishments will be brought to them soon enough ... "So leave them to plunge in vain talk and amusement until they encounter that Day of theirs which they have been promised" (Surah 70:42).
People used to say unspeakably cruel things to the Prophet Muhammad, but he never enjoined any punishment on those people. For years he was mocked, insulted, challenged, pushed out of Mecca, his companions were beaten, abused, and even killed, he was spit on, he was beaten so severely that there was blood dripping from his face, the Quraish rejoiced at the fact that all of his sons died so early, they boycotted his followers, and so on and so forth, and yet he was praying for guidance and forgiveness for the same people who were hurting him.
Here are some further logical answers that explain why the "blasphemy laws" that exist today are clearly contrary to Islam:
What is the Punishment for Blasphemy in Islam?