In this meaning, "testament" is better understood as meaning "agreement" or "deal", rather than "witness" or "account". The Old Testament involved dietary rules, sacrifices, and the like; the New Testament involves the account of the person and work and Jesus.
The New Deal often states that the purpose of the Law (the old deal) was to show that humans are imperfect (evidenced by their failure to completely and consistently comply with the law), and to cause them to realize their need for a saviour. The New Deal records what that saviour did for them, ad proposes the new plan.
In Christian teachings, those who lived under the Old Deal recognized their imperfection, and made sacrifices as a symbol of looking forward to the actions of the saviour (the Messiah), while those under the new deal look back on the actions of the saviour. Both the Old Deal and New Deal are focused on human imperfection and the need for salvation.
The Old Deal had many rules that are no longer necessary under the New Deal, due to the fact that the saviour has already come and gone. New traditions have been implemented, however, such as baptism and Holy Communion, which are also both symbols of the actions of the saviour.
It is unfortunate, as you mentioned, that many people claim to be agents of God's wrath and commit atrocities in the name of their religion. Really, it's quite a large misunderstanding. The New Deal certainly does not condone condemning unbelievers or "sinners". John 3:17, the verse immediately following the most well-known Bible verse, is very clear about Jesus not being about condemnation.
Sadly, many ignorant and misguided people have either misused, misunderstood, or manipulated something originally intended for good to justify acts of evil. To be fair, though, many people do the same with a great many things - medicines, sex, alcohol, patriotism, providing for one's family.
[A prime example of misguided people - the whole homosexual marriage issue - the New Testament (Old as well) makes it clear that while homosexuality is considered sin, so are many other things - drunkeness, lying, laziness, slander, adultery, and so on - a certain few people, though, decided that homosexuality was "worse" than other sins, though nowhere in the New "Deal" is that indicated. Certain people are just more vocal about certain issues than others, and as the saying goes, the squeaky wheel gets the grease.]