What are some cruel and unusual punishments for my character to perform to his servant?
Basically, it's a modern setting. My character is an arrogant man-child spy who has a large amount of resentment towards his servant. His servant is an old man who has reluctantly sworn loyalty to him despite a large amount of cruelties.
That kind of just sounds like you're just playing as Archer.
I guess you could just rewatch the show for ideas. No offense, but it doesn't exactly sound like you're worried about not coming off as original.
I think your character is dumb. Nevertheless, what I think does not matter, and I think a table of punishments is silly and fun, so how about this:
-Order the servant to take off his shoes and put them back on the wrong feet.
-Invite your servant to dinner. Make a delicious home-cooked meal for to. Eat your portion. Feed the other portion to the dog.
Order him to not shave for several days until his facial hair is around 1/4inch in length, at which point he should inform your character and then pluck out each hair individually using tweezers, with a 2hr deadline. This will be rather painful (a fact that you can verify for yourself) and he will have to work quickly to avoid further punishment - you could make this more difficult by giving him additional tasks to complete at the same time.
For each 1/2hr over the deadline, he will then have to pluck every hair on a limb of his choice: left or right leg, left or right arm or torso (only if he has chest hair), with a deadline of 3hrs for legs and 2hrs for arms (torso is 2-3 depending on how hairy).
Should he exceed the deadline on any one limb, he will have to pluck all of his nose hairs (with no deadline). This is very painful.
The best punishments are going to be petty ones. Not ones that cause too much lasting harm or will really fuck someone up, but the kind of petty things you'd see from a schoolyard bully. Like ordering him to build an elaborate sandcastle just so you can kick it down. Then kick sand in his eyes. Then pour sand down his pants.
Shit like that.