Is it possible to delete from multiple tables in the same SQL statement?

Question

Nope, you’d need to run multiple statements.

Because you need to delete from two tables, consider creating a temp table of the matching ids:

SELECT U.Id INTO #RecordsToDelete
FROM Users U
   JOIN LinkingTable J ON U.Id = J.U_Id
...

And then delete from each of the tables:

DELETE FROM Users 
WHERE Id IN (SELECT Id FROM #RecordsToDelete)

DELETE FROM LinkingTable
WHERE Id IN (SELECT Id FROM #RecordsToDelete)