Why don't we stone people? The bible many times specifically tell us to stone people...

Yet, I have yet to meet someone that defends that practice.

I've heard many times that this is because the OT is not valid anymore because Jesus have fulfilled it, the problem with that argument, is that then you can argue that several OT-only sins are not sin anymore.

I saw many atheists winning arguments calling us hypocrites for not following several parts of Leviticus (that for example says male homosexuals should get stone), and when I ask about it, people tell me that those are not valid anymore because of the new covenant, but for example bestiality (sex with animals) are only forbidden there... Thus if it is not valid, we cannot say to anyone that having sex with animals is a sin.

EDIT: Question not duplicate, because I am asking specifically about stoning, not the whole law in 'general', also the answer for that question is unclear on this case anyway, they decide what they must keep, but don't decide what punishments they must keep, for example "adultery" has stoning as punishment, the answer of the other question says that laws on sexual issues are kept, thus stoning would still be valid.
Both the Gospels and the Epistles repeatedly establish the New Covenant as a non-legalistic relationship with God --a new relationship not founded in following specific rules.  

However, as Paul says, not everything that is allowed is beneficial.  As a Christian, you need to be guided by your relationship with Christ and by a spirit of discernment to understand what is and is not beneficial to your mission of being an instrument of God's love in the world.  Unfortunately sometimes Christians do disagree strongly with each other on moral issues --that's just a fact of life.

In specific regards to stoning, we have additional guidance in the form of two mentions of the practice in the New Testament.  Once, when Jesus is invited to join in the stoning, and is instead merciful, and the other time, when Stephen becomes the first Christian martyr though being stoned to death by friends of Saul/Paul.  Both of these passages guide us towards rejecting stoning and the judgment that it represents.  (Some Christians, including myself, view it as guiding us away from capital punishment in general, but this is controversial).