This sounds absurd, but I've removed about a dozen moles from my chest area over the past month with a nail clipper and some rubbing alcohol.
I feel strange recommending what could be perceived roughly as self-mutilation, but it works! And you won't have scars like you would if a dermatologist removed them professionally. The dermatologist-induced scars vaguely look like minor versions of gunshot wounds.
Note that I don't remove all of a mole in one go; I sort of chip away until I'm happy. One potential pitfall is that once the surface part of the mole (the darkest bit) is removed, there's still sort of a "stain" beneath it, which won't go away entirely, although I'm pretty sure I did this a couple times when I was a little kid, and the "stains" have lightened substantially.
Anyway, in another couple weeks, if I keep at it, I'll have removed the last few moles from my chest, without any "micracle ointments" or surgical procedures that my insurance won't cover because the mole isn't "potentially cancerous."
I take no responsibility if you try this, bite too deep with the nail clipper, and scar yourself or cause an infection!