What workouts should you do at the gym to cut weight?

Weight loss and calorie burn through exercise is mainly about getting and keeping your heart rate up. And pretty much all kinds of consistent activites, like running, bicycling, swimming, dancing etc etc does a better job of keeping your heart rate up than lifting weights does. If you can lift weights at a high enough intensity and long enough to match the pulse rate and duration of a run, they you'll burn the same amount of calories. But odds are you can't. I can do around 1000 cal/hour during intense cardio, but find it really difficult to get past 600 while doing weight training. Keep in mind that the big thing is your diet. If you are overeating it's pretty much impossible to exercise hard enough to lose anything that way. A snack that takes 5 minutes to eat, like a cupcake, can take one hour to burn off.

If you insist, you should do fairly low weights and plenty of repetitions, exercises that boosts your heart rate and keeps it up consistently. Not something that's done in two big grunts and then over with.