From the Model Mayhem FAQ:

How do I delete tags from my profile?
To delete a tag, please click on the 'See All Tags' button at the bottom of your main profile page. Once all of your tags are visible, you will then see the 'Delete' button in each tag box. Just click delete on the tags you wish to remove!

Please note: We are currently experiencing a cache issue with removing tags. Although you may delete them from your tags page, they may still appear on your main profile page until a new tag is posted. Our tech team is aware of this and is working on a fix. You can force this to update by having someone else post a new tag on your profile.