Does God encourage hurting or killing others in his name in the Bible? In the Quran there is this passage: 


  And when the sacred months have passed, then kill the polytheists wherever you find them and capture them and besiege them and sit in wait for them at every place of ambush. (Quran 9:5)


As seen here, extremist interpretations of this verse push Islamists towards violence against others.

Does the Bible have anything similar to this, encouraging hurting or killing people who defy God?

I know there is Matthew 10:14-15, but that is reserved for the Judgement day.

So is there any place in the Bible where God encourages or commands others to be harmed or killed in His name?
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), bestiality (Exodus 22:19), adultery (Leviticus 20:10), homosexuality (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, &quot;when the priesthood is changed, the law must be changed also&quot;. 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.