At the White Mountain Open, I was given a backhanded compliment along the lines of "you're old and slow(er) but you still get way open. How?" After kicking him in the groin, I explained to him that it was all about positioning and knowing when to just run.
Good defensive positioning is a dynamic process. What might be good position at one point is suddenly way out of position a few seconds later as the disc is swung or the players move a few yards. The defender basically decides what cut is not a threat to the team and so doesn't have to respect that cut. Examples: player 50 yards away, a deep pass is not a threat, defender plays in front. Cutter at the back of the endzone, only cut is back to the disc, defender plays in front. Marker takes away dump pass, handler defender doesn't overcommit on a cut to the dump. The defender will follow if the cutter goes to those places, but the defender won't try to beat the cutter there.
So, what you do on offense is to try to change the position so that the defender either continues in their relative positioning (thus opening up what was previously not a threatening cut) or alters their positioning (thus opening up the cut they were trying to prevent at first). For instance, you are handling, standing about 10 yards directly in front of the thrower, being forced one direction, say, forehand. The inside-out is a very tough throw here, and the around break will take long enough to deliver that the continuation isn't that much of a threat, so a good defender will position himself to allow you to cut inside-out. What you do, then, is to take several steps to the open side. If the defender keeps the same relative position, the inside-out cut is now wide open and is an easy throw straight up the field, and a threat to deliver a continuation pass. If the defender adjusts to be more in front of you instead of to the side, you may be able to cut back to the disc for a swing or laterally for a leading "away" pass.
Downfield, you are more likely to work in/out positioning rather than side-to-side. Say the disc is being walked in, and you are planning on cutting first. Put yourself somewhere near the middle or middle-back of the stack. Prior to check in, you reposition yourself further back in the stack, slightly on the open side. By starting out in the middle, the defender will usually adopt a position that at a minimum respects the deep cut (and sometimes even takes it away and concedes the in-cut). As you get deeper, they will usually maintain the same relative position to you, but suddenly the deep cut is not an option, and the in-cut is that much more open. A smart defender will adjust at this point, but amazingly, there aren't that many smart defenders out there [insert general disparaging comment about the intelligence of defensive players versus offensive players]. In the last couple steps before you actually cut, you can also drift more out into the open, making it more of a straight shot clear of poachers. Then simply plant and run hard to the disc. You may also throw in a step away or right at the defender before cutting in, but it's just one step, and you are not waiting for a reaction from the defender before going.
(This is what I have previously called a "quick fake", where you do a fake and continue on to your real cut or throw without waiting for a response. A quick fake is a diversion. A "slow fake" involves making a motion and then reacting to the defender's response. A bunch of back-and-forth jukes from a handler is a slow fake (even if those jukes are quick), because the handler is waiting for a sign that a defender has overcommitted or not reacted before deciding where to go. Sometimes a quick fake becomes a slow fake. A thrower might lift the disc suddenly to set up a low breakmark forehand (the quick fake), but if the defender anticipates correctly and shuts off that forehand, the thrower pivots to the backhand break (the slow fake). A cutter is on the open side and has both short and long open. Do a quick fake out to set up the in cut, go hard in for two or three steps and then read the defender's reaction. If the defender has anticipated the in-cut and has maybe even overcommitted to that, you immediately stop and cut deep as hard as you can.)
Sometimes, through no effort on your part, an "opportunity cut" will present itself. Maybe you're in the stack a little on the open side, your defender is fronting you and not watching the disc at all. At that moment, you're not a deep threat because the disc is not in a position to be hucked. However, you see a swing pass go off to the open side and the receiver is someone who can huck it. Suddenly, you're in great position to cut deep, provided that your defender keeps his focus on you. Allow him to do that by pretending to prepare for your own in-cut. Then, you make a hard step in and immediately reverse and cut deep. The defender will be backing up and even if he is faster than you, you will have enough of a head start that it shouldn't matter.
So, the basic idea is that you need to identify an area that you would like to cut to, then purposefully walk (or shuffle, or run if you must, I suppose) in the opposite direction, giving the defender the opportunity to make a mistake in positioning.