Saturate a cloth in hot water. Rub the sloppy paint with the cloth. Continue rubbing the paint and saturating the cloth in hot water until you have removed the sloppy paint from the cabinets.
Saturate a corner of a cloth with rubbing alcohol. Rub the sloppy paint with the saturated cloth. Continue applying the rubbing alcohol and scrubbing the sloppy paint until you have removed it from the cabinets.
Fill a bucket with 1-gallon of warm water and 1/3 cup of trisodium phosphate. Scrub the cabinets with a sponge saturated with the mixture. Continue scrubbing until the paint is removed.
Scrape the sloppy paint off the cabinets using a paint scraper. Place the edge of the paint scraper at the edge of the paint. Apply pressure to the paint scraper and push forward. After each pass, wipe the paint scraper clean with a paper towel. Scraping the paint off of the cabinets could damage the cabinet's finish. You may have to stain and refinish any areas of the cabinets damaged by the paint scraper.
Rub the sloppy paint with a cloth saturated with turpentine. Turpentine is highly flammable and must be kept away from open flames and sparks. Use the turpentine only in a well-ventilated area. Wipe the turpentine off of the cabinets with a clean cloth dampened in cool water. Turpentine can damage your cabinet's finish, so care must be taken when using it.