Note: You can also use this function to cut individual faces, because they are treated as open objects. See Cutting Multiple Faces by One Object.
The part shown below consists of three individual solid objects.
Required Step 1 
Select one or more objects (open or closed) to be cut. In this case, select the light blue and dark blue objects. Note that these objects are rectangular and elliptical prisms, despite the presence of the magenta object. Press exit when all objects are selected.
Required Step 2
Toggle the Separate Objects/Don't Separate Objects button as required and select the cutting tool, in this case the magenta solid. Press exit.
Note: If more than one object is selected for cutting, you can only pick one object as the cutting tool. However, any number of objects created from the same sketch are considered as one object. Also, merged objects and those created using Solid / Add functions are also considered one object. Example:
Press OK 
or Apply 
in the Feature
Guide to complete the function.
Note the resultant shapes of both blue solid objects.
To further demonstrate the results of this function, move the magenta object. The light blue and dark blue objects have each been cut.
When completed, the Cut appears in the Feature Tree as follows:
