Cutting things is a very common task when crafting things in real life, but also a well-known operation in the digital world. In terms of cutting and pasting files, that's a rather symbolic way of applying the concept, however when it comes to design, people often want to cut images in a more literal or at least visual way.
The tools of image editing softwares are often based on real tools and features, just like the Pen or Brush Tool. However, when I wanted to cut a shape in Photoshop once, I unsuccessfully searched for a Scissors or Knife Tool. Some people might think of the Slice Tool now, but that's only helpful for subdividing the document. I recognized that there's no easy, direct way of cutting shapes, so I kept experimenting with this specific use case.
For better understanding, I'll show the goal and steps to get there in a simple example:
If you had to cut the rectangle above as a raster image, this would be a pretty easy job: Just draw a selection, and hit Ctrl+X to cut it. Since raster graphics are just a grid of pixels, Photoshop simply has to remove all pixels inside the selection. In contrast, vector graphics are based on mathematical expressions, or thinking more geometrically, they're made up of 2D points connected by lines or curves.
Of course you could simply rasterize the shape in Photoshop before splitting it up. That's a bad idea though, because you'd lose valuable benefits of using shapes, such as smaller file size or blur-free upscaling.
At this point it's worth mentioning, that Adobe Photoshop is mainly used for raster graphics and its counterpart Adobe Illustrator is generally a way better choice for working with vector graphics. In Illustrator, there are more dedicated methods of cutting shapes, however the additional cost might not be worth it for designers, who only have the photography subscription.
So let's start cutting that rectangle in Photoshop. There are different approaches which I will explain consecutively.
Manually Adjusting the Path Points
The first intuition might be to drag the two points on the left to the position where you want the cut to be. A shape's path can be edited after clicking it while holding the Ctrl key (Cmd on Mac). Keeping Ctrl pressed, you can then drag a path point using your mouse. This can get fiddly at times, so also holding the Shift key really helps by limiting the movement to 45°-axes.
Done! Well, at least for this specific use case and only one side of it. If there were more points to the left, you would have to delete all of them. More critically, the method above doesn't work as perfectly for curved shapes.
As a side note, all shapes in Photoshop are based on so called Bezier Curves. This might be confusing at first as the example only consists of straight lines, so here's a quick explanation: Bezier Curves are made up of control points, whereas the first and the last are the start and end points and the other ones determine the curve flow. In Photoshop terminology, each path point (also called anchor point) has two more control points for the left and right direction. In case of the rectangle, Photoshop only displays the anchor point because the directional points are equal to it.
If we apply the method above to a circle, its overall shape will get messed up:
As you can see, we've only moved the anchor points, not the directional points. Adjusting these to fit the original curve flow on the right side of the cut line would be super tedious and imprecise.
A slightly better approach is to add new path points at the cutline, deleting unwanted points afterwards. Using the Pen Tool, clicking on a point will remove it and clicking on a path section without a point will add one. You can then see that added points have two control points, even when on a straight line. (Photoshop calculates them to fit the current path flow)
Dragging the ones on the left side over to the anchor point will give you the cut shape. In case of the rectangle, you can also Alt+Click an anchor point to move both directional points to its position. Unfortunately there's no shortcut for just resetting one of them, so for the circle you'd still have to manually move them.
With a few steps, you can cut shapes along a simple line like that. In the next chapter I'll explain a more universal approach which also works with more complex cuts.
Combining Shapes Using Set Operations
Photoshop offers four methods to combine multiple shapes. These are sometimes referred to under different terms, such as set, path, shape or boolean operations. Photoshop quickly calculates the resulting path information which lets you create more complex shapes with a few clicks. With two shape layers selected, you can access the operations via Layer -> Combine Shapes. Below is an overview of how each of them works.
Its worth pointing out that you can also have multiple sub paths on one shape layer. This comes in handy because you can change the type of operation for added paths in any path tool's settings at the top:
Setting it to Subtract Front Shape makes it possible to directly delete areas from a shape for example by drawing a path with the pen tool.
To clean things up, click the Merge Shape Components option, which will leave you with only the new path resulting from the operation. That's it - once you get a grasp of set operations, cutting shapes is a pretty easy task. One more thing to consider is that when you combine separate shape layers, the new shape will always have the attributes (color, stroke, etc) of the topmost layer. If that's not what you want, plan ahead and copy the shape attributes before applying the operation and paste them afterwards.
Automating Repetitive Cutting Steps
For people who need to cut many shapes, switching between set operations and drawing boxes can become repetitive and annoying steps that slow down the workflow. I've also noticed, that sometimes you don't want to cut and delete a part, but simply split a shape into separate layers instead. Using the techniques explained before, you'd have to copy the shape layer, cut out one side and then repeat it the other way round to get the inverted result.
Since I had recently started implementing Photoshop extensions, I thought that this would be a great use case for an add-on. So I've created Easy Cut, a small panel which makes it easier to cut not just shapes, but any type of layer.
Easy Cut lets you cut layers either along a guideline, path or selection. Besides that, I've added an event system which checks for specific actions like adding a new guide to trigger the cutting automatically. You can turn each of them on/off depending on personal preference. Check out this short demonstration video if you want to see the panel in action:
Wrapping up
Before working with shapes in Photoshop, it's helpful to understand the fundamentals of how they actually work. Each path point actually consists of a set of three points - one anchor point and two directional points. You can drag these around holding down Ctrl/Cmd to adjust the outline of a shape, however this can become quite fiddly very quick.
To cut shapes, a much more efficient workflow is to utilize set operations which offer a way of combining multiple shapes. If you want to speed up this specific task even more, you can make use of external add-ons to do the repetitive steps for you.