MySQL 8.0

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CREATE TABLE `test`( jsdata JSON)
 
INSERT INTO `test` VALUES
('[
    {"a": "1", "b": "2"},
    {"a": "1", "b": "-2"},
    {"a": "2", "b": "1"},
    {"a": "2", "b": "-3"},
    {"a": "3", "b": "4"}
]')
WITH RECURSIVE cte AS
(
 SELECT 0 i
  UNION ALL
 SELECT i + 1 i
   FROM cte
  WHERE i + 1 < ( SELECT JSON_LENGTH(jsdata) FROM `test` )  
)
SELECT JSON_PRETTY(JSON_ARRAYAGG(JSON_EXTRACT(jsdata, CONCAT('$[',i,']')))) AS Result
  FROM `test`,
       cte
 WHERE JSON_EXTRACT(jsdata, CONCAT('$[',i,'].a')) != "1"      


Result


[
  {
    "a": "2",
    "b": "1"
  },
  {
    "a": "2",
    "b": "-3"
  },
  {
    "a": "3",
    "b": "4"
  }
]