take the blame for sb.

take在这里表示“承受”的意思，blame是“责备”之义；for sb./sth. 是介词短语，表示“为某人”，整个短语就是“为他人承受责备”，就是“背锅”。

Why should I take the blame for others? 

我为什么要代人受过？

to become a scapegoat for sb.

我不应该成为他的替罪羊。

I don't deserve to become a scapegoat for him.