I'd use something like this long before I try cutting anything, whether it be the motherboard slot or the video card's PCB:
Amazon.com: StarTech.com PCI Express X1 to X16 Low Profile Slot Extension Adapter (PEX1TO162): Electronics
As for performance, there's definitely a drop:
Ivy Bridge PCI-Express Scaling with HD 7970 and GTX 680 Review | techPowerUp
If you look at the original post, he used Team Fortress 2 with unknown resolution or setting to claim there's no problem, and it's a GeForce 8400GS, which can probably be beaten by Intel 2500 Graphics...