From their help pages:
1. Login to your Mint.com account.
2. Click on the Your Profile link at the top of the page.
3. Click the Settings icon in the toolbar of the window that opens.
4. Scroll to the bottom of the page and click the red link to Delete Your Mint Account.
5. Click YES, delete my Mint Account.
6. Type your password to confirm, and then click on Finish.
7. The confirmation box will appear stating that your account has been deleted and the confirmation email will be sent to you shortly. Click OK.