This is a topic that has come up and will probably come up again, so I am going to explain how I view these words.
Modification: a change made to ones body that one desires for the sake of the change itself. Eg, tattoos, piercings, scarification.
Mutilation: a change made to ones body that is not made with consent (either because consent is not given, or cannot be given [if the person is too young for consent]). Eg, circumcision in babies, tattoos or body alteration made under duress or when a person is unable to consent.
There are certain other things that could potentially fall into both categories, but I will explain my views those as they come up.