I use the following:
DECLARE @ConstraintName varchar(255);
SELECT @ConstraintName = CONSTRAINT_NAME
FROM
INFORMATION_SCHEMA.CONSTRAINT_COLUMN_USAGE
WHERE
DECLARE @constraintName VARCHAR(50);
DECLARE @runString VARCHAR(2000);
select @constraintName = CONSTRAINT_NAME
from INFORMATION_SCHEMA.CONSTRAINT_COLUMN_USAGE
WHERE TABLE_NAME = 'TheTable' AND COLUMN_NAME = 'TheColumn';
SET @runString = CONCAT('ALTER TABLE TheTable DROP CONSTRAINT ', @constraintName);
PREPARE stmt1 FROM @runString ;
EXECUTE stm1;
DEALLOCATE PREPARE stmt1;