You can only remove players in between rounds, sorry. A player with games still going on cannot be removed. Unfortunately, nothing can be done in this situation.
Removing player from a tournament

One thing you could do is block the user. That would at least prevent him in entering in any tournaments you host in the future.
http://support.chess.com/Knowledgebase/Article/View/38/1/how-can-i-block-another-user

Puchiko: the problem is, you can't kick out a player in between rounds that is the last in every round =/
DanaEileithyia: Thanks, this will come in handy.
Godspawn: Yeah, I recently created a no vacation tournament.
Is there no way I can report this to the chess.com staff and have them adjudicate the game?

Create a No Vacation tournament next time.
Well as tournaments can run for months some players do want to have the ability to use vacation, certainly when the summer holidays becomes closer and they might be without an internet connection for 1-2 weeks.
The problem however seems to be the players abusing it. If someone who plays actively, goes to vacation for a week, states in his status something like, "Holiday in Spain - back 1 July". Almost no one would have a problem with waiting a bit for the next round.
However someone abusing it and going to vacation just to delay the tournament and opponents is something entirely different in my opinion and another solution has to be sought for this. Though the option of no vacation tournaments is off course good for the player who do not need vacation anyway.

I considered asking the opponent. It would suck because the opponent would lose a lot of points on resigning that game (1880 vs. 1350 or something) but he's also guaranteed to make it to the next round, so I guess it all depends on what his priorities are. Maybe a draw offer would work too.

Meh, dont give the griefer a reward. Tough it out, block the kid, and keep asking the staff at chess.com to help.
They may be staff, but they are still human, and some part of them has to be seething at this person.

by wasting your time you are giving him a reward. resigning would be the best way to beat himon my opinion.

By resigning, it's true, you'd be the bigger man, but on the other hand, the other guy might see it as an incentive to continue the behavior.

Is there anyway for chess.com staff to step in? It's been a month since the second to last game ended (which was also this same player's)
The staff won't do anything, it'd be too open to abuse. If they started adjudicating even the most obvious cases of abusing vacation time, they'd soon be flooded with requests to adjudicate all kinds of "won" positions. All you can do is accept that vacation time can and will be abused. I don't think you'll have problems finding players for a non-vacation tournament, in this day and age people can access the internet practically anywhere.

Ok, I guess I'lljust let it go. He has been moving now, albeit very slowly. I can only hope he either A) runs out of vacation time, B) Sees the light and resigns or C) starts playing quicker. Hopefully, he'll be mated pretty quickly. His opponent still has a wall of three connected passed pawns to push to promotion.
Hi all! I'm running a tournament in which someone has been playing both of their simultaneous games considerably slower than anyone else, has abused vacation time and is dragging out his final remaining game in a lost position against a much stronger opponent, preventing the tournament from moving on to the next round. I sent him a message regarding the torunament and his game and asked that he respectfully resign or finish the game quickly. Not only did he not comply, but I never even got a reply from him, I know for a fact he has been online several time and has played and finished games, but he has not even made a move in his current game.
I tried to remove him from the tournament to allow it to progress, but it tells me I can't withdraw a player with unfinished games remaining. Then what's the point? It's my tournament, I find his conduct disrespectful to me and all the other players and seeing as the bracket result is already decided and his game is lost against a much stronger opponent (the highest rating in the tourney) I feel I should have the right to remove him. How can I go about doing this? He could drag this on for another month if I let him and I have gotten numerous complaints from the players.