Follow whatever training protocol you have. There is no need to change your lifting if you have found a program that works for you. You could less rest between sets or do more supersets to make your training more intense. You could also add in HIIT or LISS. HIIT may be too taxing on your body when cutting, depending on the routine. For example, if you are following a PPL routine, HIIT may be too much. I do like the idea, posted above, of jump roping between sets or even doing plate carries between sets.
Keep in mind, focus on your heavy compounds. You want to keep your strength as high as possible.