According to the Idioms Dictionary,to burn one's bridges (behind one) means:
1. Lit. to cutoff the way back to where you came from, making it impossible to retreat. The army, which had burned its bridges behind it, couldn't go back. By blowing up the road, the spies had burned their bridges behind them.
2. Fig. to act unpleasantly in a situation that you are leaving, ensuring that you'll never be welcome to return. If you get mad and quit your job, you'll be burning your bridges behind you. No sense burning your bridges. Be polite and leave quietly.
3. Fig. to make decisions that cannot be changed in the future. If you drop out of school now, you'll be burning your bridges behind you.You're too young to burn your bridges that way.
Ou seja: to do harm to past relationships,"sair pela porta dos fundos" deixando uma imagem desagradável e rompendo com o passado, o que poderá fechar as portas ("queimar as pontes" em inglês) caso precise/queira um dia reatar com aquelas pessoas ou retomar tais relações.