I'm on an HP Envy 15-3040NR with an AMD Radeon HD 7690M graphics card (also an Intel card for dual graphics). When I run certain games (e.g Bastion, Awesomenauts, Battlefield 1942 with Wine) the mouse pointer has a couple seconds of delay. In Bastion, moving the mouse over a menu icon will result in the menu sound effect being played a second or two before the graphical cursor actually moves. Other games run just fine with no lag, like Red Eclipse, Vega Strike, and Teeworlds.

I'm running Linux Mint Debian Edition, updated to Debian Sid. Fglrx (AKA AMD Catalyst) is version 13.4, I've tried the 13.6 beta with no effect. Xorg version is 1.12, MATE is my DE.

I've Googled the problem, most answers seem to relate with V-Sync. I've tried enabling and disabling v-sync both in each game and with "aticonfig --initial --vs=off". Nothing seems to have any effect. Any ideas?

I went close to buying one of those, but the price was crazy here. You now have a nightmare on your hands. You will have to make friends with the graphics switching stuff, update it if you can as it is continually being developed, and then make some findings.
1. Which GPU is doing the work you don't like? That (probably) has a hdmi port which (probably) is connected to the HD7690. Does the same thing happen out there?
2. Is wine slowing you down? There are video settings for wine (under winecfg). The game might see no directX installed - find the trick to get over that. If you haven't got it, get winetricks.
3. Are there issues with fglrx and that card, or that game (phoronix.com forums to find out).
4. Is power saving or conservative scheduling in the kernel slowing the box? Is the cpu doing the full whack?
5. Can you balance the load between cpus better?

Don't guess the answers to any of that stuff. But if you can't nail one, try the rest anyhow.

EDIT: Debian is rock stable, but not new. You will probably do better on a different distro - a more bleeding edge type thing. The only one I know is fedora, but I am sure there are others.