There are two methods you can follow to duplicate an existing Project.
One method is to open up the Project you wish to duplicate. When you're on the Summary screen, open up the overflow menu. You will see a "Duplicate" option. Tap this and you can decide what data you wish to include in the duplicated project (by default, all data will be duplicated but you have the choice to exclude Issue Photos, Assignees, Tittles and Comments). Tap duplicate and you will be taken to this duplicated Project.
An alternative method is to hit the + button at the top of the screen to bring up the Create New Project screen. From there you have two options highlighted at the top of the screen. One is to 'Create new project' and the other is 'Create from existing'.
If you choose 'Create from existing', the first option on screen will allow you to select an existing project to duplicate data from. Once chosen you can edit the relevant fields and then tap the tick icon in the top right.
The app will then copy all data from that existing project to the new project.