I use the following:
DECLARE @ConstraintName varchar(255);
SELECT @ConstraintName = CONSTRAINT_NAME
FROM
INFORMATION_SCHEMA.CONSTRAINT_COLUMN_USAGE
WHERE
Try this
SELECT CONSTRAINT_NAME INTO @ConstraintName
FROM
INFORMATION_SCHEMA.CONSTRAINT_COLUMN_USAGE
WHERE
TABLE_NAME = 'TheTable'
AND COLUMN_NAME = 'TheColumn';
SET @queryStr = CONCAT('alter table TheTable drop constraint ', @ConstraintName);
PREPARE qry from @queryStr;
EXECUTE qry;
For more information: https://dev.mysql.com/doc/refman/5.7/en/execute.html