Slapping with a lighter touch is a good start, but also try to minimize your movements. You can get your thumb up to speed in less than an inch, there's no need to start the movement from a hitchhiker's thumb position
Less movement means more speed and precision, which will clean up your slap (sound).
You also need to dampen the strings, with either the left hand fingers and/or the right hand palm. It's kinda hard to explain, it'll come with practice.