Hi Maxim,
You can make a copy of the project and run it locally. However when you commit to the team server/deploy to the cloud from the copied project, it will (most likely) just act the same as your ‘original’ project, thus overwriting your current deployed version.
What you can do however is use the ‘export project package’ option from the business modeler, then start a new team server enabled project and after creating the project; use the ‘import project file’ option in the modeler of the newly created project.