Another word for “twist and squeeze” could be “wring”. This verb captures the idea of twisting and compressing something, often to extract liquid or to tightly manipulate an object. For example, you might wring a wet cloth to get the water out.
Depending on the context, “squeeze” and “twist” can also be replaced with words like “wrench”, “press”, or “contort”, which all imply applying force in various ways to alter the shape or structure of an object. Each of these alternatives carries a slightly different nuance, so the best choice depends on the specific action or effect you are describing.