The process is straight forward within DesignSpark PCB, open your project which you wish to create a new version of. Here we have our current project "CopperPourTestV2" as an example.
With the project tab active select "Save As" from the file menu.
To keep the new project self contained in its own folder, create a new folder appropriately named and give the projects a Project name within that folder.
Here we have named the folder "Controller MkII" and gave the DesignSpark PCB project the same name. Left click "Save" and project is created.
Next we are presented with the options to save the original schematic and PCB files to this project folder and the opportunity to rename at the same time.
Overtype the file name as required for the schematic file an left click "Save".
Repeat for the PCB.
In this example each was renamed to "Controller MkII", left clicking "Save" completes the process and DesignSpark PCB is ready with the new project and the appropriate files.
The original project remains intact and you can now continue your design work on each project independently.