Does grass die if there is grass clippings on top on it?

Yes and no. Some modern lawnmowers are designed to 'mulch' the grass. That is, when used without the grass collection box/bag, they chop the clippings very fine and dump them on the lawn as you mow. This, if done every second or third cut, actually helps the lawn by feeding it. The grass needs to be quite short already to do this. If it is too long the mower will continually clog. If you leave heavy grass clippings on you lawn you will prevent light from reaching the grass and therefore stop photosynthesis and the grass under the clippings will die.