expression, godan verb (-ru)
bring disgrace on; put to shame; fling mud at
Idiomatic expression meaning to cause someone to lose face or be publicly humiliated. The image is of smearing mud on someone's face, i.e., dirtying their reputation.
彼の不正が家族の顔に泥を塗った。
His misconduct brought disgrace on his family.
そんなことをしたら、先生の顔に泥を塗ることになるよ。
If you do that, you'll put your teacher to shame.