Long press the widget until it releases and then drag it off to the trash/remove area. It usually turns red when you have the icon in trash can.
That will take Mint off your screen. If you want to delete it completely, it all depends upon what phone and what OS you have. However, this way I'm about to give you is true for all Smartphones. Tap on the menu key, then on Settings>Applications>Manage Applications. Next scroll down to Mint and tap on it, and then tap on uninstall. If you have a phone running on ICS, then you will see Apps. Tap on that and scroll down to Mint and delete it. Personally, I tried Mint, which is an Intuit (Quicken) product and didn't like it at all. Have you tried Easy Money? They have both a free version and one that costs a few bucks. I got the paid version and really like it.