Fat does leave your body through sweat and other ways through your body when you burn off fat.
So yes in a way you can technically sweat out some of your fat from your body.
When you exercise and begin to sweat the exercise along with the sweating allows you to burn off body fat and burn calories.
Then as you sweat the body fat leaves your body through the sweat through metabolism process that is very complicated.
You also lose body fat through urine, feces, your breath etc.
So your body fat leaves your body through feces, sweat, breathe and urine and a lot of other ways.