Winner of my giveaway suspended

Can you contact him through steam?
This is the only option,because you send the key so you can't reroll...

nothing

Good god. He won that DLC four times.

I'd say the two are totally separate items - him winning the giveaway which you've already sent and then him getting suspended for whatever reason - don't do anything

it's your fault, why didn't you check if he already won the game??

Nothing to do about it. If he doesn't (or can't) mark it as received you could contact support to remove the giveaway but they wont do a reroll since you can't be sure if the key still works (new winner might receive used key + give you bad feedback).

It is possible that this guy entered multiple drawings for the same DLC and then was suspended. If that happened, he wouldn't be able to withdraw any entries because he wouldn't be able to log into the site. In any case, you have already sent him the key.

There are a few different ways you can approach this. One is to contact Support and talk to them, find out what they think you should do. Another is to try and redirect the key, somehow. (Do you have a friend who can redeem it to his or her inventory?) Yet another option is to just throw up your hands and say, "Hey, it's my fault I didn't check out the winner before sending the key, so I guess this is going to be a learning experience for me."

Something like that happened to me on my first giveaway, though I was the one who got him suspended (should have checked his profile first, but I was new to the site and I thought that if he had won the game already, he wouldn't be able to enter another giveaway).
What I did was pick another user that had entered, contact him through steam and give him the key.

I would of suggested to request a reroll, but since your already given him the key, depends if used or not... no way to check?

Is it against the rules to enter multiple giveaways for the same item?

The odds you'll win more than one are pretty low. Especially since you can always withdraw from giveaways if you win one and get your points back.

DO A KEY DROP. Don't let the shit head profiteer.