The phrase "slice up" refers to cutting something into small, thin pieces. There are plenty of synonyms for this phrase depending on the context. "Dice" is commonly used when cutting vegetables or fruits into small cubes. "Chop" is used when separating a large food item into smaller pieces with a sharp tool like a knife or an axe. "Cut into strips" is used when you need thin, long pieces such as cutting meat or fish. "Minced" is used when food needs to be finely cut into small pieces and often required by recipes for seasoning. "Shred" is used when you want thin, ribbon-like pieces and is often used when shredding cheese or cabbage.