Spray the area around your machine (up in the air and let the mist disperse over a wide area). You can also use a spray bottle of water that creates a very fine mist in the air when sprayed. Purchase a vaporizer, usually used for sinus congestion relief, and place it near the area of your machine (anywhere in the same room, but not too close as to create water droplets on your vinyl). The another recommendation might sound weird, but works better than anything else to reduce the buildup of static electricity.
There are also antistatic sprays that you can use to spray on the backing paper before you load it into the machine, but they can get messy real quick. Another solution is to use clothes dryer sheets, such as Bounce, by rubbing it on the vinyl to be cut, before you start cutting. Static electricity build up and the subsequent discharge will be reduced. The first being, slow your cutting speed, so the machine doesn't move the vinyl through the rollers as fast. There are a few things that I can recommend to overcome this issue. Memory chips inside the machine are prone to be affected, which throws off the programming on them as well as the commands sent to the cutter by the software. Touching the machine while it's cutting, and causing a small spark between your hand and the machine is a definite indicator that static electricity is the culprit. This issue is more prevailant during the winter, when the humidity in the vicinity of the machine is reduced by central heating. It is caused by the backing paper of the vinyl being rubbed across the faces of the machine during the cutting process and gets worse the faster your machine moves and cuts the vinyl. I've also experienced the static electricity problem you described in your first post. This doesn't make much sense either though, since the machine's power plug contains a ground to that (through the electrical plug) already.
I believe the correct or more proper way to ground it would be to use a wire connected to the stand (or the bottom of the machine) in which the other end of the wire would connect to an earth ground, such as the screw holding an outlet cover on. I've often questioned the grounding method explained above, since the machine is grounded to the stand by the 4 screws that hold it onto the stand.