Be aware that many properties have utility easements (or rights-of-way) that providers run their cables through. If your existing cable was run using such an easement, this could present a couple of problems for you:
- The hole you want to dig would appear to be inside the easement. Utility companies are allowed free access to that easement, which means if they need to they can dig up your tree or break your pool or whatever you're using that hole for.
- Other utilities are likely using the same easement. As you try to move this line, you'll have to be extra careful not to disturb any other buried utilities running alongside it. You could also run into more esoteric problems like signal quality issues due to moving a poorly-shielded communications cable too close to an AC power line.
If you aren't sure about the location of utility easements on your land, check the survey for your property. If you didn't get a copy when you bought the house, you can usually get one from your city/county records office (wherever property deeds are recorded).
If you do decide to try this, I recommend using the smallest tool possible. Any sort of digging/trenching power tool would eat through the cable without flinching. Even a regular shovel is pretty risky. Depending on your soil composition, I'd recommend something like a garden trowel, at least until you know for sure where the cable is. Many communication cables are not actually buried that deep (regardless of how deep you think the trench was). A flood washed away about a half-inch of soil on one side of my house, and that was enough to expose my buried cable TV line in places even though the trench they dug when installing it appeared much deeper.
Even if your yard was pure sand, I doubt you'll be able to pull any of that slack while the cable is still buried. You'll likely have to dig up the entire cable, starting at where the cable leaves the house and continuing to just beyond the spot where you want to dig the hole. The good part is that your risk of cutting the cable is low. You don't have to guess where it is, you'll be able to see it as you're digging. The bad part is that you have a lot of digging ahead of you. It's probably enough work to make it worth re-evaluating how badly you need that hole in that exact location.
If you're digging this hole to plant a tree, make sure you install a root barrier between the tree and the buried utilities. Otherwise, you're planting a time bomb that can generate very expensive repair bills at some random time in the future.