That is the best way to make any woody shrub look wretched and ugly. If you do that, you might as well have them removed, because big shrubs can take decades to grow out of that, or they can be weakened enough they never really recover.
It’s really hard to explain, but the best way to revitalize a shrub and make it look more natural is to do proper pruning (as opposed to trimming or hedging).
But, here’s a technique as outlined in “The Landscaping Revolution: Garden With Mother Nature, Not Against her”:
You’ll need two pruners: a long handled pair about two feet (60cm) long, and a smaller one handled pruner, about nine inches (25cm) long.
Now, check the trunks. If two are growing into eachother and are rubbing off the bark (providing an opening for infection), keep the trunk that is growing outward, and remove the one that is growing inward. Cut it back to ground level.
Check the aesthetic quality of the trunks that are left. Be very cautious about taking out trunks that are not potential problems. Have someone pull the trunk in question as far out of the way as possible, so you can see how the tree will look without it. If you’re still in doubt, leave it. You can always remove it later, but you can’t glue it back.
Now, start cutting off all the branches that grow in toward the center of the tree. Cut every one of them off at the collar – that’s the slight thickening of the branch where it joins a larger branch or trunk. The idea is to give the tree a nice, airy, open feel in the middle.
If the branches have been hedged or hacked back so many times that the branching looks like a starburst of mini branches (a very ugly look), cut back to the first long, undamaged branch that points outward.
Do not cut off the end of a branch for at least five years; this allows the branches to grow long enough to give your yaupon (a holly), or whatever, a treelinke structure. After five years, if your tree is as large as you want, you can begin cutting off end branches – but always cut them off at a collar. Do not just snip off the end.
The main idea is to open the plant up and give it a natural feel. Opening it up also helps to prevent diseases or simple mildew (which is what dark, dense interiors can allow).
You also want to remove any dead branches. You can check this by scraping a little bit of the bark off to check for either green cambium or fresh, moist whitish looking wood. If the wood has gone brown or gray, it’s a dead branch. Esepcially if you bend it and it snaps with a a dryness. Living wood usually has a good amount of give before it snaps off (and sometimes it won’t without a struggle).
I’m not sure what kind of tree you have. Are the leaves in needles, or are they broad and spiny? The former would mean yew, the later would mean Holly. Although many other plants have red berries and are used as hedges, like Pyracantha (Firethorn).
When I prune, I usually prune off branches so that you get the remaining branches alternating, rather than keeping them and allowing for the branches to be alternatate (paired). Here’s what i mean: alternate branch pruning
This manner of pruning really helps to give plants with a natural herringbone branch pattern a more “wild” look.