The critical consideration is whether there is some of the handle extending above the butt of your hands, at the wrists. You probably want at least one to two inches here, so your hands are down on the grip material a bit, although not all the way to the metal below the grip material. If you extend your index fingers down the shaft, the length of most hands from heel of hand to tip of index finger is around 7 inches. I believe grips come in a set length of about 10 inches. This leaves one inch from fingertip to metal and two inches from heel butt to top of handle. So usually, you want your hands down below the top of the handle a little -- there's room built in for this.
Another consideration is having some of the handle extend above your hands so you can watch this part of the putter. If your stroke motion is too abrupt or quick, the top of the handle will waggle, indicating that the PIVOT of the putting system is not in your neck, but inside your grip! And that ain't good. So there needs to be a bit of the grip above your hands to help monitor your stroke's pace and fluidity.
Another consideration is the irreversible nature of cutting the putter. It's better to err on the side of too long, since you can always grip down. But if you err by cutting the putter too short, you're forced to use a setup posture and stroke movement that you really didn't want. Figuring this out takes some time for adjustment and experimentation, so I advise not cutting a putter all that short until you live with something that looks 2-4 inches too long for a little while. If the putter is working okay, don't cut it any further. Only cut it further if the excess length is definitely too much and somehow bothering you and you're sure you have no use for it. And remember, sometimes you want to putt while standing a little straighter, just for variety or to experiment or to give your back a little rest.
On balance, keeping the short putter a little long is a good way to strike this balance. And it's also a good idea to start with a cheap second-hand putter to cut down, so if you make a goof it's no big loss.