In the method copySheetTab of SheetAPI, it allows user copy the existing sheet tab and create a new one. .
Here comes the code example
var store = SHEET_API_HD.store;
SHEET_API.copySheetTab(SHEET_API_HD, store.getActivedSheetId(),
'new tab name',
function(){
alert("Successfully copied");
}
);
The above code will copy the currently active tab and create a new tab with input defined name.