To start an entirely new project use the standard Windows command of 'File' from the top menu bar and then 'New Project'. You will be prompted to save the current project if you have not done so.
I've not got Video Easy but the product description states that you can "Burn several movies to one DVD..." and "You can also make separate menus for each film...". This function may be the cause of your inability to reduce the sive of you project by deleting scenes. When you open a project in other Magix editing programs you get the option to add it to the current project. If you have (perhaps without realizing it) created a project with multiple movies, the total size is very like so big that the removal of a few scenes will have no noticeable effect.