Ask Mr. Smarty Plants

Frankly, we're astonished that you HAVE grass under your canopy of oaks. We have dealt with the problem of things growing under oaks several times recently. See this previous answer, dated August 26, 2009, on why plants won't grow under oaks. Another, on ground cover under oaks, dated February 24, 2009. This excerpt from an answer dated Dec. 10, 2008 specifically addresses the failure of grass to grow beneath oaks:

"In general, plants need light (for photosynthesis), water (for photosynthesis and other processes), and minerals (which also help in photosynthesis). The grass growing under your pin oaks could be suffering from lack of sunshine, and it is certainly competing with the oaks for water and nutrients. The shade problem isn't easy to solve, but you can increase the amount of water and nutrients that the grass is receiving. Is the die back new, or has it been going on for some time? If it is new, you might try to determine what conditions have changed?"

Need we go on? You didn't say what kind of grass you have, probably it is non-native St. Augustine if it is surviving at all in all that shade. We don't like non-native grasses, obviously, but this may be a case of "if it ain't broke, don't fix it." If you want to have a go at it, the mulch would be okay, as long as you didn't get it up around the trunk of the tree, where it might encourage fungi and rot. It is an attractive ground cover under a tree, won't smother the roots and, as it decomposes, will in effect be composted to amend and enrich the soil. The newspapers could be another story, and from personal experience, the top layer of mulch tends to get kicked or blown around, and suddenly you are looking at the Sunday funnies and car advertisements all over your property. And they are blowing around too, which isn't going to endear you to your neighbors.  If we were going to advise you on the best way to rid yourself of the grass, yes, pulling it out is the best way. And pulling it out, and pulling it out and pulling.... Grass can be very persistent and, again from personal experience, St. Augustine gets along just fine under mulch. It may be a little paler green from being covered by mulch, but IT'S ALIVE.