I have a star made on the canvas, but I can't find a standard selection box to select only half and then delete it.
Alternatively, you can keep your shape vector and cut it in half leaving it node-editable and more useful with either of two easy approaches:
1. Boolean Operation
Draw out a rectangle shape over the part you wish to subtract, snapping to points to get it exactly located. Click the Subtraction Boolean icon in the toolbar above, and the item which is in front will be subtracted from the item behind.
As you can see here, switching to the Node Selection tool you can tell this is still vector - hasn't been rasterised - and is thus far more useful overall.
2. Convert to Curves
Select your shape, and click the Convert to Curves button on the toolbar above. this takes away the automated shape controllers, but make the resulting vector curve node-by-node editable.
Use the Node Selection tool and drag a rectangular marquee over half your nodes to select them - like so:
Then hit the Delete key on your keyboard - this will be your result:
Which should get you what you need with far greater operational flexibility than rasterising your layer; there are cases where rasterising is not only called for but super-helpful, but in general I tend to keep things vector as much as possible.
Hope this helps.
First: put the vector (star image) on that background and press "Enter" Then go to the layer option and then select your vector layer. Right click on that, then press "Resterize layer" Second: use "Rectangular Marquee Tool" to cut your vector according to your will. Cutting technique: select the half of your vector with "Rectangular Marquee Tool" and press [Ctrl with x]