SQL Server 2014

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WITH
  data AS (SELECT CAST('{"f1":["v1","v2"],"f2":"v3"}' AS varchar(max)) AS ResponseJSON),
  parser AS
  (
    SELECT
      Level         = 1,
      OpenClose     = 1,
      P             = p.P,
      S             = SUBSTRING(d.ResponseJSON, 1, NULLIF(p.P, 0) - 1),
      C             = SUBSTRING(d.ResponseJSON, NULLIF(p.P, 0), 1),
      ResponseJSON  = SUBSTRING(d.ResponseJSON, NULLIF(p.P, 0) + 1, 999999)
    FROM
      data AS d
      CROSS APPLY (SELECT PATINDEX('%[[{]%', d.ResponseJSON)) AS p (P)
    UNION ALL
    SELECT
      Level         = ISNULL(d.OpenClose - 1, 0) + d.Level + ISNULL(oc.OpenClose, 0),
      OpenClose     = oc.OpenClose,
      P             = d.P + ISNULL(p.P, 0),
      S             = SUBSTRING(d.ResponseJSON, 1, p.P - 1),
      C             = c.C,
      ResponseJSON  = SUBSTRING(d.ResponseJSON, p.P + 1, 999999)
    FROM
      parser AS d
      CROSS APPLY (VALUES (NULLIF(PATINDEX('%[[{}:,]%', d.ResponseJSON), 0), NULLIF(PATINDEX('%]%', d.ResponseJSON), 0))) AS p_ (a, b)
      CROSS APPLY (VALUES (CASE WHEN p_.a < p_.b OR p_.b IS NULL THEN p_.a ELSE p_.b END)) AS p (P)
      CROSS APPLY (SELECT SUBSTRING(d.ResponseJSON, p.P, 1)) AS c (C)
      CROSS APPLY (SELECT CASE WHEN c.C IN ('[', '{') THEN 1 WHEN c.C IN (']', '}') THEN 0 END) AS oc (OpenClose)
    WHERE 1=1
      AND p.P <> 0
  )
SELECT
  *
FROM
  parser
OPTION
  (MAXRECURSION 0)
;

Level	OpenClose	P	S	C	ResponseJSON
1	1	1		{	"f1":["v1","v2"],"f2":"v3"}
1	null	6	"f1"	:	["v1","v2"],"f2":"v3"}
2	1	7		[	"v1","v2"],"f2":"v3"}
2	null	12	"v1"	,	"v2"],"f2":"v3"}
2	0	17	"v2"	]	,"f2":"v3"}
1	null	18		,	"f2":"v3"}
1	null	23	"f2"	:	"v3"}
1	0	28	"v3"	}