When you open up a character's inventory, at the top left of it you should see a circular button with a persn and an arrow. Click on that to disband the selected character. You will get a confirmation box to ask if you really want to disband that character, and in the case of disbanding pets you also have the option to release the pet back into the wild (in which case you will never see it again).
You can collect disbanded characters and pets from the inn back at town if you decide you want them back again.
From cradle to coffin... Shall my wickedness... Be your passion