A Cut Stroke is an off-plane
The ideal putting stroke stays on plane. While your putter path is less important than your putterface angle, it can still adversely influence the direction of your putt.
A Cut Stroke is where your putter path travels from outside your aimline (target line) to inside your aimline. In other words your putter swings off plane and cuts across your aimline.
The question is:
WHY does this matter as long as your putterface is perpendicular to your aimline when your putter meets the ball?
Research and Testing has shown that there are two fundamental alignments that influence the direction your ball travels after you make contact with it.
The first is your putterface angle and the second is your putter path. Rik DeGunther in his book The Art and Science of Putting calculates that the ratio of influence is around 15% putter path and 85% angle of impact.
Your putter path therefore plays a small, yet significant, part in the accuracy of your putts as any error in path is transmitted to the roll of your ball. David Leadbetter estimates that three out of four recreational golfers slice not only their full-swing shots, they slice their putts as well.
The ideal putter path imparts zero side-spin to your ball as side-spin has a negative effect on how soon your ball achieves true roll.
However, it is possible, but not desirable, to get your ball to travel more or less along your aimline with an outside-to-in putter path and a slightly open face on contact.
Early instructional texts on putting mention little or nothing about putter paths as the topic was largely irrelevant. Golfers putted with their wrists. There was no movement of their arms and shoulders.
With golfers using a pendulum motion as a more reliable way to putt on smoother and faster greens, the problem of the putter wandering all over the place is a real possibility. Therefore to manage your putting stroke, you need to pay careful attention to setting up correctly at address and staying connected until the ball is on its way.
Here are some reasons why your putter path can follow an errant outside-to-in direction that produces a cut stroke.
While you want to avoid a cut stroke that slices across your aimline, you should steer clear of another bad habit of watching the movement of your putter.
Be confident that with good alignment, a correct ball position, and a stroke that moves your shoulders, arms and hands in unison, your putter path will stay on plane, and not cut across your aimline.
1 = Illustration from Dave Pelz's Putting Bible
2 = www.quintic.com