How do I disconnect from a previous project, so that I can start a new project. I was invited by others on the previous project, so am hesitant in just deleting my stuff which they may still need.
Hi @Jim_Junio and welcome to the Forum 
From what I understand, you were invited to a project in your colleagues’ Workspace/Organization. You can create your own Workspace/Organization following these steps:
Workspace: Workspace basics | Product guide • Asana Product Guide
Organization: Setting up an organization in Asana | Product guide • Asana Product Guide
Once you have created your own space, you will be able to create and start working on your own projects. You will also be able to easily switch between your own space and the one you were invited to, but if you wish to, you will also be able to leave the space you were invited to (Workspace basics | Product guide • Asana Product Guide Setting up an organization in Asana | Product guide • Asana Product Guide)
If you’re unsure what a Workspace and an Organization are, have a look at this handy article.
Hope this helps! Let us know if you have any questions
Can you change the project owner to someone other than yourself, then have them reassign the tasks (or remove you as an assignee). That should keep the tasks intact in the previous project.