Does the gospel of Matthew promote self-harming?

No it does not. Try to understand that some of these parables are not to be taken literally. Jesus is not teaching self mutilation in this scripture, the lesson is that we deal drastically with sin. Self discipline. Live the Holy Life; 1st Thessalonians 47-8 " God did not call us to be impure but to live the Holy Life. Therefore he who rejects this instruction does not reject man but God who gives you his Holy Spirit." Don't give in to temptation, remember what Jesus told the devil on the mountain; Matthew 4:10 " Away from me Satan, for it is written worship the Lord your God and serve him only."