Sounds like he is testing boundaries (totally normal for his age). Try ignoring bad behavior, and in the case of throwing his cup, take it away/remove the opportunity/hold him still and say no firmly, but don't look at him or give him any extra attention. Same for biting, hitting, or anything else.
But maybe--is he getting enough sleep? I know you say he will do this even after a nap, but whenever my little one doesn't get enough rest, he becomes a little monster (normally very sweet and lovey). At this age, they should be getting 1-2 naps of about 1 1/2 hours and going to bed around 6:30 PM, waking up around 6-7 AM.
Also pay attention to what you are feeding him. In addition to the usual culprits of sugar and caffeine, there have been some findings about food coloring causing crazy behavior. Even if he is just eating lots of carbs on their own, he might be having sugar crashes. Try to give him mini meals with a fat, protein, and carb (snack for mine is often cheese and crackers or cheese and fruit, or yogurt). Aim for 3 meals plus 2 snacks.
If sleep and diet don't fix it, read Raising Your Spirited Child. It may be that he is feeding off your stress in a very bad feedback loop. Or that he is over stimulated.
Good luck. Don't worry, this is a totally normal problem and you will definitely find a solution. It will just take a little patience.