When an original owner co-owns a project they uploaded with you, you don't have the ability to delete the project. However, you have the option to remove it from your profile. Go to My Profile > Hover over the project you want removed > Click the Pencil Icon > Click Remove.
NB: if you only see the option to Delete, you are the original owner. Clicking Delete will completely delete the project for everyone. Deleted projects cannot be recovered.
The project will be removed from your profile and you will no longer have access to edit it. However, it will still be visible on other co-owner's profiles.