To disgrace someone; to tarnish someone's reputation (literally: to throw mud on someone's face).
不正行為の発覚は社長の顔に泥を塗った。
The discovery of the misconduct disgraced the company president.
そんな嘘をつくと、友人の顔に泥を塗ることになるよ。
If you tell such lies, you'll be bringing shame upon your friend.
家族の恥になるような行為で、祖父の顔に泥を塗ってはいけない。
Don't do anything that would disgrace the family and bring shame on your grandfather.