You can make the freshly cut glass safer to handle by gently wiping the edges of the cut piece with the waste piece. This removes the sharpest edges without chipping the glass.
After the glass is scored and broken, you can remove small, unwanted chips with grozing pliers. The serrated jaws of these pliers are used to gently nibble away at the jagged edges.
Rough edges can also be smoothed with a carborundum stone. You rub the stone along each edge, upper and lower, to remove any sharp edges. You can remove more glass with the stone if you wish by a little more aggressive grinding action or just a longer light rubbing of the stone against the edges.
A diamond smoothing pad removes glass in much the same way as a carborundum stone, but does it more quickly with the coarser grades. You can use a number of grades to get an almost bright polish to the edges. These pads must be used with water.
A glass grinder is used by many people. Many models of grinders are available. The grinding surface of the bit is covered with fine diamonds, which grind away unwanted glass very quickly without chipping the edges. In addition, they are water-fed which keeps the glass from cracking due to heat, prolonging the life of the diamond bit, and preventing the powdery ground glass form flying around.
A glass grinder is not a substitute for accurate cutting.