When someone says something mean to you or speaks ill of you, instead of taking in the harsh words and internalizing them as true of you, go to Jesus and ask Him to show you what lie that person is believing about themselves. Since our harsh words toward others are reflections of what we believe about ourselves projected and displaced, the lie He shows you will be something along the lines of what they are saying about you or to you. After you understand their lie belief, ask Jesus to show you the truth about you, to help clean out any places their lie has tried to inhabit in you.
Recognize the same thing is true of harsh thoughts, feelings, and words you have toward others. Instead of speaking them, look first in the mirror and ask Jesus to show you the source of the harsh words in a lie you believe about yourself. Then, ask Him what the truth is about you. Finally, ask for the truth about the other person - how He sees them - and allow His truth to take over your harsh thoughts and feelings.