As a verb, maul means (1) to injure by or as if by beating, or (2) to lacerate. The word is also a noun referring to a heavy hammer.
Mull, which is only a verb, is a synonym of ponder, often used with over. So mull is the correct spelling in the common phrase mull over. Maul is the correct spelling in reference to violent attacks.
A third homophone, mall, is only a noun, primarily referring to a large shopping complex containing a variety of businesses.
I was frantic when he didn’t call after a week, imagining he was dead, sick or had been mauled by a wild beast. [Canada.com]
To put the mauling into perspective, consider that Purdue had allowed more than 70 points just three times in 33 games. [Chicago Tribune]
An off-duty policeman has spoken of how he saved a woman from being mauled by a German shepherd. [BBC News]
While some athletes would mull endlessly on such a decision, Matthews answered it emphatically. [Herald Sun]
Lindsay Lohan is spending some time away from Los Angeles to mull over her current legal woes. [Daily Mail]
She is reportedly mulling options, including a syndicated daily talk show. [Los Angeles Times]