@maehaa , The FixMat is made of Static-Dissipative materials, meaning that any accumulated charge will disperse across the surface of the mat and there won't be any localized voltage differences across the mat.
If the mat were connected to a grounding point, the mat would then be grounded. You can do this with an alligator clip or other means of connecting a conductive wire to the surface of the mat.
If you choose to not ground the mat, you can equalize the voltage between the device your working on and the mat simply by touching the device (before you've started taking it apart) and the mat at the same time.
You can also ground yourself to the FixMat using our ESD wrist straps.