[Note: this is an expanded version from the blog entry from May 10.]
This is the forehand serve where you serve with the racket tip up, and contact the ball on the right side so it curves to the left, and the spin makes the ball come to your right off the opponent's paddle. It's awkward for many to take a ball spinning away from them on the forehand side and aim to their right, especially if the ball is short - try it and you'll see. Until you reach the advanced levels, nearly everyone returns this serve crosscourt toward the opponent's forehand side, and often they miss by going off the side to their left, or they allow the opponent to camp out on the forehand side. (This is for two righties; lefties make the usual adjustments.)
Now think about this. Have you ever missed returning this serve by returning off the right side? Probably not. So just take it down the line, to the backhand, knowing the sidespin will keep you from going off the side. Contact the back of the ball, perhaps slightly on the left side, so that the ball goes to the right, down the line.
Keep the racket relatively high - don't lower it as you chase after it as it bounces and spins away from you, or you'll end up lifting the ball high or off the end. Better still, don't chase after it - anticipate the ball jumping away from you and be waiting for it, like a hunter ambushing his prey. It's often this last-second reaching for the ball that both loses control and forces the receiver to hit the ball on the right side, thereby making down-the-line returns impossible, with many returns going off the side to the left.
When the tomahawk serve is deep, it is often easier to loop down the line because by doing so you don't have to overcome the incoming sidespin so much. When looping this type of sidespin crosscourt you contact the ball somewhat on the far side (the right side of the ball), going with the incoming spin, and so you have to overpower it. It's almost like looping against a backspin. If you take it down the line, you contact the ball more on the back, and so you are going against the spin, and so it's like looping a topspin. Just as when looping against topspin you don't have to lift the ball much when going down the line, so the table isn't in the way, and you don't have to overcome the incoming spin as you'd do against a backspin.
Because the table is in the way, many players compensate by rolling the ball back softly. If you place it well, you can get away with this. However, another way to handle this is to loop it aggressively, so you don't have to lower the racket below table level, so the table isn't in your way. This especially works if you loop crosscourt, since you may be able to backswing from the right side of the table. If you loop down the line the table may get in the way a bit more. As noted in the previous paragraph, the key when going crosscourt is that you have to overcome the incoming spin with your own topspin.
Finally, if you simply can't do anything aggressive with this serve, use placement and deception. Aim one way, and at the last second return the serve softly (and perhaps quicker off the bounce) the other way. For example, aim to the server's forehand, which is where he expects it, and then at the last second just pat the ball down the line. This pretty much takes the server's forehand out of play. If his backhand is stronger, try the reverse.
Note that the tomahawk serve is rarely used at the higher levels. (Though there are a few who specialize in it.) There's a reason for this; it's generally easier to read the spin off this serve (the wrist motion is more limited) and there's generally less variation than from other serves. Sure, you might have trouble with this serve the first few times an opponent pulls it on you. But after you've seen it a few times, and made adjustments, you should be able to take the initiative off this serve, and force most servers to use other serves.