MySQL catch exception and log it into another table for example.

mysql_catch_transaction_exception_block.sql

# CREATE PROCEDURE AND OTHER DECLARE STATEMENTS HERE
# ....

DECLARE EXIT HANDLER FOR SQLEXCEPTION
BEGIN
    GET DIAGNOSTICS CONDITION 1 @sqlstate = RETURNED_SQLSTATE, @errno = MYSQL_ERRNO, @text = MESSAGE_TEXT;

    ROLLBACK;

    SET @full_error = CONCAT('ERR:', @errno, '(', @sqlstate, '):', @text);

    CALL sp_logaction(@full_error); # Some logging procedure

    RESIGNAL;
END;
# PROCEDURE BODY WITH START TRANSACTION & COMMIT HERE
# .....