Same other versions as well.
There is no one delete button that wipes away the project file (.prel) and the project's assets. You need to go to the save locations of the project file (.prel) and its assets and delete
each one by one wherever they are saved UNLESS you pre-plan and, before the project is created, set up a particular project so that the project file with assets goes to its own folder instead of each component of the project going into a common place for Premiere Elements files and folder where you have to pick out the materials for deletion one by one by name.
Default type situation
If left at defaults and if your Premiere Elements 13 is running on Windows 7, 8, or 8.1 64 bit, go to Libraries/Documents/Adobe/Premiere Elements/13.0 and, in the 13.0 Folder, delete standalone files with your target project's name and delete files with your target project's name in the folders found in the 13.0 Folder.
Edit Menu/Preference/Scratch Disks - Set all to Same As Project.
Create a new folder at a hard drive location of choice.Then point the project file to that folder for the Save In.
Tip: When the Expert workspace of the new project opens, go to File Menu/Save As. Name the project and set the new folder created as the Save In of the Save Project dialog.
Please review and consider and then let us know if any of that worked for you.