Assume that each patient only has one DRG CODE. Try this:
SELECT t1.PATNO,
SUM([Billed Charges]) AS BilledCharges,
t2.[DRG Rate],
t2.[DRG CODE] AS [DRG],
CASE WHEN SUM([Billed Charges]) > 275000 THEN (SUM([Billed Charges] - 275000) * 0.195 + t2.[DRG Rate] ELSE NULL END [Stop Loss],
CASE WHEN SUM([Billed Charges]) > 275000 THEN (SUM([Billed Charges] - 275000) * 0.195 + t2.[DRG Rate] ELSE t2.[DRG Rate] END [Claim Total]
FROM Table1 AS t1
INNER JOIN Table2 AS t2 ON t2.[DRG CODE] = t1.DRG
GROUP BY t1.PATNO, t2.[DRG Rate], t2.[DRG CODE];