After opening your project click on the "more" toolbar button in the upper right corner of the main panel, and select the "Delete" menu option (highlighted) and then the sub-menu option "Delete this document".

If a task was either selected or opened when you opted to delete your project you will get a prompt asking you if you meant to delete the entire project and all of its tasks, or just the task you selected. Click on the appropriate button to delete the entire project and all tasks (1) or just the selected task (2).

When a project is deleted all the tasks within that project are also deleted. You cannot delete a project if billable time or expenses have been recorded against any of the tasks. In this case either mark the project as complete or transfer tasks that you need to keep to a new project first and then delete the project and its remaining tasks.

You can also delete a project from the search list by selecting the project you want to delete and then clicking the upper right "more" button and selecting the menu option "Delete" and "Delete this Document" (highlighted).

Click here to find out how to undelete a deleted document.