You can put drywall mud over paint to fix a bad mud job as long as you employ the appropriate preparation techniques. Employ the proper repair strategy, or the mud will not adhere.
Drywall mud is used to affix drywall tape over areas where sections meet, effectively promoting an even, seamless appearance. This process is called taping and bedding. When this task is performed incorrectly, cracks may appear and tape may peel away from the drywall.
Most wall paint contains chemicals that promote a sheen. This makes the paint ill suited for adhesion. If you apply drywall mud directly over underprepared existing paint, it will not adhere properly.
Abrade the existing paint to promote adhesion. Scour the paint with a fine, 280-grit sandpaper, before you apply the drywall mud. Once the paint feels slightly rough to the touch, it will accept the fresh drywall mud.