It is OK to add shredded paper, grass clipping, and shredded tree leaves to the compost pile. All of these will break down and turn into usable compost. However, mixing these materials with dirt will slow down the composting process. They will still break down, but it will take something like a year, as opposed to a month or two in a compost pile. If you want to set up your raised beds immediately, and you want to add organic material to the clay soil and improve the texture, then you will have to get some finished compost, or use peat moss, or something similar. However, if you want to set up your raised beds this fall, and you don't plan to plant anything there until next spring, then it might make sense to mix in un-composted paper and grass clippings at this time.

If you can sift it, I have to wonder if it is primarily clay. The clay soils I have encountered don't sift well. You just screen out rocks and most of the soil as big hard chunks of clay. Have you done a soil structure test with a jar of water yet?

Also, where are you so TX can look up your soil profile, lol.

How quickly your soil would "break down" the newspaper and grass clipping mix will depend on how active a Soil Food Web that soil has, and whether that soil is in good condition, ie. a soil pH and other nutrients in a range tht is good.
Contact your state universities Cooperative Extension Service about having a good, reliable soil test done for soil pH and major nutrient levels and maybe use these simple soil tests,
1) Soil test for organic matter. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. For example, a good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top.

2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drainsâ too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up.

3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart.

4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer your soil will smell.

5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.
for more information about that soil.

It's fall, so what I would do is remove the gravel and whatnot, mix in some finished compost (you can buy a bag or three if you need to, just remember you generally get what you pay for). Rake it out and then cover it with a mixture of your compostables. Make it as thick as you want. This will do several things. It will of course compost at least somewhat over the winter. The soil will be protected from rains and freeze/thaw, and the worms will even come up to get the organic mulch, which will help enrich and aerate. By doing your digging now, the clay will have all winter to recover from it and develop some structure.

In spring, you can plant through the mulch (tomatoes or other starts), or remove as much as you need to and put it into the compost pile.

This works pretty well for my clay, YMMV.

I live in southern California and it's still viable right now to grow cole crops. I do have a pH tester that I can use to check the acidity and I can get a jar and do that test as well. For sure though the next thing I need to do is screed out the rocks.Thanks for the advice everyone and I will keep you all updated with the direction we are going with the raised garden bed. For sake of expediency I might end up buying bags of compost from the local hardware store.

When you fill your raised bed with a mixture of compost and soil, you can expect it to settle considerably in the next 6 months. To end up with the soil level where you want it next spring, it might have to be 6 or 8 inches higher than normal this fall. That's just a guess, though...

If you till that soil you will introduce air into the mix which will raise the level some depending on how much air is entrained. As moisture forces that air out from between the soil particles the soil will settle. This is why soils are always allowed to sit and settle after tilling and before planting.
The experience many of us have had with those inexpensive pH meters is they are not very reliable. I have seen some that give the same reading whether testing a baking soda mix or vinegar, you probably should not get a 7.3 pH reading from either one.