When the liver is taxed, it can’t process toxins and fat in an efficient way. There are many foods that can help cleanse the liver naturally by stimulating its natural ability to clean toxic waste from the body.ips For Doing a Liver Cleanse. Other liver cleanse foods not listed above include artichoke, asparagus, kale, and brussel sprouts. Eating the foods listed above is a great way to help keep your liver functioning properly.