Decomposing the splitter function might not give the best performance, but it could help in your case.

--Create sample data
CREATE TABLE #Sample ( SomeColumn varchar(1000))
INSERT INTO #Sample
VALUES('Part 1/Part 2/Part 3/Part 4/Part 5/Part 6/Part 7/Part 8/Part 9');

--The solution starts here
WITH E1(N) AS (
      SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1 UNION ALL
      SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1 UNION ALL
      SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1
      ),         --10E+1 or 10 rows
   E2(N) AS (SELECT 1 FROM E1 a, E1 b), --10E+2 or 100 rows
   E4(N) AS (SELECT 1 FROM E2 a, E2 b) --10E+4 or 10,000 rows max
SELECT *
FROM #Sample
CROSS APPLY(
    SELECT ItemNumber = ROW_NUMBER() OVER(ORDER BY s.N1),
       Item = SUBSTRING(SomeColumn,s.N1,ISNULL(NULLIF((LEAD(s.N1,1,1) OVER (ORDER BY s.N1) - 1),0)-s.N1,8000))
    FROM (--==== This returns N+1 (starting position of each "element" just once for each delimiter)
       SELECT t.N+1
       FROM (
          SELECT 0 UNION ALL
          SELECT TOP (DATALENGTH(ISNULL(SomeColumn,1))) ROW_NUMBER() OVER (ORDER BY (SELECT NULL)) FROM E4
        ) t(N)
       WHERE (SUBSTRING(SomeColumn,t.N,1) = '/' OR t.N = 0)
       ) s(N1)
    )s
WHERE s.ItemNumber = 6;