There are almost never seedlings growing from acorns. If there were, you would be able to pull them up easily. What you see are sprouts from the roots of the existing tree; therefore, you do not want to spray a herbicide on them in an attempt to eliminate the sprouts for you will hurt the “mother” tree along with the sprouts.
Only a small percentage of oaks send up suckers from the roots. It is a genetic trait, like freckles, except I like freckles. But like freckles and sunshine, some trees have the ability to sucker, but do not unless stimulated to do so. Oaks having a slight tendency to sprout suckers will often do so when roots hit a barrier, such as trees confined to a parking lot planter, or between a sidewalk and driveway. Also, when roots are disturbed and damaged by rototilling, they are more likely to sprout suckers. But some trees never will make suckers. When choosing an oak in a garden center, if there are sprouts coming up at the inside edges of the container, I would avoid that tree.
You may choose to mow them along with the grass, if grass still exists. Or if the grass has thinned too much, you might plant Asiatic Jasmine groundcover, and use hedge trimmers to trim the jasmine and oak sprouts to a uniform height. You can cover the area of sprouts with a heavy gauge woven geotextile, and then either mulch or spread large gravel or decomposed granite over the top of the geotextile. My favorite solution, when appropriate, is to cover the ground with geotextile and then build a wood deck.
Or if you prefer a thick green lawn, you may remove the oak tree, and all of the tree roots with a backhoe. If you just cut down the tree, grind down the stump and all the large roots you can see, there will still be thousands of oak sprouts emerging from the remaining roots in your new lawn or bed area for a few years afterwards. The area will need to be continually sprayed with an herbicide.
James 
james says
I wouldn’t trust A lightweight consumer type product. And don’t trust that products sold in the mass market with a commercial designation is really up to the task. Greatly exaggerated. A medium to heavy gauge woven Geo textile is likely to come on a roll from 6 to 12 foot wide by 300 foot long. Also a spun bonded material of extra heavy gaugewould be on a much larger spool than a retail type
Kat says
Where I live in the NorCal Sierra foothills, the sprouts under the oak tree are NOT from the big oaks tree roots, they are grown from the acorns. I have pulled over 300 of them this year, most with the acorn still attached, some broke off. There are probably another 600+, I really need a spray to kill them. Any ideas? I have already used Milestone, so far, no luck, the little sprouts are still growing taller every day it seems.
Rose says
Kat, You might try Eraser with dosage of 4 tablespoons to 1 gallon of water It has done wonders to get rid of Oak Volunteers in my yard. There is no residual affect to the soil and after about 48 hours it has no effect on pets. Do not use Eraser Max as it will leave a residual in the soil, possibly harm animals, and you cannot plant anything for a year or so afterwards, do not confuse the two. Keep in mind it worked on my Oak Tree Volunteer which are from the tree and have no acorn attached, but it is still worth a try? See your local distributor for your area and there are many now. They will be able to recommend the correct dosage as a double check, and they can tell you the correct dosage to spray in your area with any adjacent plants around that area. However you have to directly spray right on the plant to kill it. We have had very good luck using this product, however only time will tell how long the effects will last? Thanks.
James Gill says
I would not recommend Eraser, as the active ingredient is glyphosate, the same as Roundup. It may kill the sprouts, but some of that glyphosate can be taken into the large tree. If the amount of sprouts in relation to the massive size of the tree is pretty small, well I guess this is how the writer has not had problems. But there is danger in applying glyphosate to root sprouts.
James Gill says
Sorry Kat, I just saw that you are talking about oak SEEDLINGS, not root sprouts. You could use Eraser, or any other brand of glyphosate including Roundup. But I would be 99% sure they are not root sprouts before using glyphosate!