It was made by the female Twig girdler beetle (Oncideres cingulata).

Hosts
Common hosts of the twig girdler include persimmon, pecan, elm, hickory, oak, honeylocust, hackberry, poplar, linden, redbud, basswood, dogwood and various fruit trees.

Biology
The adult beetle is about three-fourths of an inch long, stout, grayish-brown with a lighter colored band across its elytra (wing covers) and has antennae as long as its body.

Adult beetles typically begin to emerge in mid-August and continue through early October. During this time, the adult female chews a V-shaped groove all the way around a small twig, girdling it. She then deposits an egg beneath the bark in the twig section beyond the cut (severed portion). This is because the larva is unable to develop in healthy sapwood. The cut made by the adult female is deep enough around the twig so that the girdled portion dies quickly and usually falls to the ground, either because of wind or its own weight.
Adult female twig girdler

Figure 1
Adult female twig girdler chews a V-shaped groove from the outside inward, leaving a ragged center where the twig breaks and a smooth cut on the outside near the bark

During the oviposition period, large numbers of girdled twigs often accumulate beneath the tree each day. After hatching from the egg, the developing larva bores into the dead twig to feed. The small larva will overwinter in the fallen twig. During the following spring, the larva resumes feeding, consuming most of the wood.

As the larva grows it bores further down into the twig and fills the tunnel with wood shavings and waste. Pupation occurs in a cavity within the twig. Adults emerge in late summer and early fall. Twig girdlers produce one generation a year.

Control
Homeowners should collect and destroy infested twigs and branches they find on the ground, beginning in September or no later than May. If practical, prune infested twigs still in the tree.

Owners of commercial pecan orchards should look for severed twigs, beginning in August. Apply insecticide carbaryl to trees only if you see damage. In severe cases, you may need to apply insecticide two to three times at two-week intervals. Be sure to follow label rates and directions.

Click here for an illustration and the source

We had many persimmon twigs cut off by the little pest beetles and also a few Pecan twigs at our place.
And I burned all the twigs I could reach or find on the ground.

See those little horizontal lines on the twig? Those are where the female beetle layed the eggs which will hatch larva and they feed on the dead wood of the twig until they turn into a beetle next year and the females repeat the twig cutting and egg laying each fall. So burn every twig that was cut off to kill the eggs, if they don't break off in the wind cut them off and burn them also. They cut the twigs because apparently (like read above), the larva can not develop in healthy live sapwood, they can only live in the dead dry twigs which they feed off of.

Adult beetle images:
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Full-grown larva preparing to pupate in a dead twig found on the ground:
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Oh man.....I wish it had been a bird or something easier to control. I guess I need to get busy. Maybe pecans weren't the smartest things to plant with all these hickory trees around here. Thanks for the information. Who would have ever guessed an insect did this!!! Pretty amazing. I'll remove all the damaged limbs tomorrow.