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First, I want to point out that moving itself is a decision. The key behind cutting is some combination of: keeping your defender busy, creating space for other players, and attacking space with the intention of being open for a pass. (Obviously, that list is not exhaustive.) Sometimes, not moving is the best option, counterintuitive as it may be.
All too often players cut for the sake of cutting. There are a number of problems with this: it clogs and eliminates passing lanes, it detracts from the offensive rhythm, it wastes valuable energy, it allows defenders to pay less attention to you, etc... Decisiveness is a mandatory component of effective cutting, and if you are just running around the field, chances are it's not in a decisive fashion. Decisive cutting requires that you commit 100% to the cut. That will allow you to take advantage of your offensive advantage, namely that you get to decide where to go while the defender must react to that decision. Strong defenders are able to recover quickly and stay with you on your cut. That is why you need to put the maximum amount of pressure on them by going full tilt.
Now, great defenders will anticipate where you A) want to go, and B) can go. That is one of the reasons you can't just cut anywhere. If you cut to a non-threatening area, the defender knows he doesn't have to play you close, and can lend his defensive services to a teammate. On top of that, the non-threatening space you just cut to may have been valuable real estate for one of your teammates (that is until you stupidly infringed on it).
Ultimate is truly a team game, and if you are cutting out there for yourself - whether you are just focusing on getting open for the disc or simply trying to shake your hungry defender - then you aren't playing a team game. Advancing the disc with the best risk/reward ratio is the only goal of the offence. Now, how you solve that ratio is entirely team-specific. However, there are meta-principles for all offences.
All offensive players are disc-advancers. As a cutter, you need to (not) move in the way that maximizes the range of options available to the thrower. Everyone who has played ultimate knows that feeling when you have the disc, and all the downfield players jam the open-side throwing lane right in front of you. They all rush to the obvious space where you should be able to throw an easy pass. The result is that they collectively render the throw impossible. Why? Because even though there are multiple receivers, you only have one throwing option, which happens to be into a pack of defenders who know you only have that option... And cue the turn.
The thrower should have all options at all time; the full range of angles and the full range of risk: Short and deep looks on the open-side, two dumps, a short break, and a longer (probably over the top) break. Think of these options as areas on the field, not as players occupying those areas. These areas are always there for a given disc location on the field. They may differ in size, location and risk, but they are almost always present.
So, the job of the disc-advancer can be seen to be two-fold: both enter and exit these options within the structure of the offensive system and in a productive fashion. It's how you enter and exit these spaces that determines how good a cutter you are. Recognizing who should be where, what the best combination of which players in which spaces at any given moment is - that is the incredibly difficult process that a cutter is expected to instantly, constantly, and flawlessly execute at all times when on the pitch.
And at its core, the focus is only ever partly on cutting for yourself.
those are some of my thoughts.
ps - crafts is just sick: