In the method deleteSheetTab of SheetAPI, it allows user delete the existing sheet tab. .
Here comes the code example
var store = SHEET_API_HD.store;
SHEET_API.deleteSheetTab(SHEET_API_HD, store.getActivedSheetId(), function(){
alert("Successfully delete");
});
The above code will delete the currently active sheet tab. You can also pass the sheetId to delete it.