Does God encourage hurting or killing others in his name in the Bible?

In fact not. There is no general case in all the scriptures of any such thing. The closest you will find is 1 Samuel 15 1-3, where King Saul is ordered to destroy the Amalekites. But see, this is a specific command given at a specific time with a specific target, given via a well-ordained and uncontested prophet of God. Here the standard of evidence is so high that if God were to order such a thing again he would have to send a prophet again, and seal his words with signs as was done of old.

Even if a prophet were to appear with signs and wonders and give such an order as sampled in the Koran, the counter would be Matthew 28:19 followed by Deuteronomy 13:2. No such order as kill the polytheists can be given because it is the plan of God that all nations shall have the chance to repent.

But Muhammad gave no sign.

Does God encourage hurting or killing others in his name in the Bible?

The Bible has two parts. The last part (the New Testament) is the culmination of God’s work in man such that believers can have new and eternal life in Jesus. Since Christians have God living in them, they do not need to worry about others. Even though there are those in history who have claimed to be Christian and hurt and killed others, this was in violation of what God said.

Luke 6:27 But I say unto you which hear, Love your enemies, do good to them which hate you,

The first part of the Bible (the Old Testament) is mostly a history of Israel. The laws that God gave the nation involved capital punishment for various crimes. Israel was not to impose their laws on others.

The nation of Israel was to be given land that was occupied by others. The entry of Israel into this land was delayed because the sins of the people had not yet gotten bad enough for them to be completely exterminated.

Genesis 15:16 But in the fourth generation they shall come hither again: for the iniquity of the Amorites is not yet full.

The extermination of the tribes in Canaan was similar to the extermination of life on earth during the flood. There is a limit to the evil God is willing to endure.

The problem was that Israel was not faithful to do as God asked them. They kept some alive, not out of mercy but to make their lives easier by keeping some as slaves. This introduced the evil of those who were to be exterminated into the nation of Israel.

God allowed many armies to attack Israel and Judah and finally allowed them to be taken into Babylon as captives for 70 years. When they returned, they finally stopped the practice of idolatry.

In summary, Christians are not instructed to hurt or kill anyone. In historical times Israel was to use capital punishment in their laws for themselves and they were to only exterminate those in Canaan that God had told them to.

There are a number of passages in the Old Testament where God is described as supporting the Israelites in their quest to kill or otherwise drive out the native tribes of their land, including places where God is described as forbidding or punishing mercy. Judges 6:16 would be one typical example. These are generally in what are known as the "historical books." It's possible to view these as attitudes that the ancient Israelites are misattributing to God, but in terms of actual verbiage, they are not all that distant from the Quran passage quoted above.

There are some pretty bloodthirsty Psalms as well, although those are typically addressed TO God, not presented as from God.

There are no passages in the New Testament where Jesus or the Apostles promote violence (other than when Peter attacks a guard and is immediately rebuked by Jesus). Jesus does say he comes "not to bring peace, but a sword" in Matthew 10:34. This passage is never, however, read as a exhortation to violence, but rather as a prophecy of coming turmoil attending the establishment of the Christian religion and/or the apocalypse. In general, the rejection of violence, and the establishment of a communion of persons of all nations and cultures is one of the most stark and striking differences between the Old Covenant scriptures and the New Covenant scriptures.

Short answer

There is not a single passage in the New Testment that even encourages phisical violence against others.

Long answer

Yes, at the Old Testment you have some instructions that involves death penalty, for example, for murder (Exodus 21:12), kidnapping (Exodus 21:16), be*t**lity (Exodus 22:19), adultery (Leviticus 20:10), h*m*sexuality (Leviticus 20:13), being a false prophet (Deuteronomy 13:5), and so forward.

But now, you have to understand that all this penalties were restricted to the context of the nation of Israel, at the time of the Law, and this all was a glimpse of God's moral standards. But when Christ comes at the plenty of time, when it comes to the New Testment, like says the Author of the book of Hebrews, "when the priesthood is changed, the law must be changed also". You now notice that all violence now is figuratively turn to the self, no more to the other.

You are told not to persecute, but to love the ones that persecute you.

If you suffer for the Name of the Lord, you don't repay, you rejoice.

You don't have to strike others, but to stike yourself (figurativelly, of course).

If someone do you harm, the Lord will give repay (not you in the name of the lord).

If someone blaspheme, you just hand them to Satan, not by killing them, but by simply removing them from communion.

The thing here is: you have no mention in the NT to, personally, do phisical harm to another. This idea is even contrary to the whole premise of the NT teaching. Instead, you have lot of instruction to suffer the harm for love of the other.

External resource

And, finally, here is a great article with a comparision of Violence found in Bible x Violence found in Quran (This article is great dealing even with the Old Testment violence). There, i think, you'll find a solid base to answer your real question.