As a first class entity, Teams can be associated to Stories, Epics and Iterations in Shortcut.
While a Story dialog is open, you may select the the appropriate Team via the dropdown in the upper right hand corner. When you assign a Story to a Team, each dropdown within an Epic, Iteration and Owner will be prioritized based on the Team:
Similar to stories, Epics can be assigned to a Team. Simply navigate to that Epic's detail page and select the correct team from the right hand side panel. Stories within an Epic inherit that Epic's currently assigned Team by default. However, you can still associate Stories within this Epic to a different Team if needed. This cross-Team relationship is highlighted by Shortcut via the exclamation icon on the Story's dialog as well as the Story table within the Epic:
All entities can only be associated directly with one Team (i.e. Two Teams cannot be added onto the same Story, Epic, or Iteration).