When an SqlError is thrown, an error is raised in MySQL similar to how one is raised by a SIGNAL statement. You can create an SqlError using the constructor shown here:

new SqlError(
  sql_state: Number, 
  message: String, 
  error_number: Number
)

The JavaScript stored procedure in the following example tries and throws an SqlError created using this constructor. Invoking the procedure raises the error, as can be seen here:

mysql> CREATE PROCEDURE test_catch_throw_signal() LANGUAGE JAVASCRIPT
    -> AS $$
    $>     console.clear()
    $>   try {
    $>     throw new mysql.SQLError(45000, 'Some error', 1001)
    $>   } catch (e) {
    $>     console.log(e)
    $>   }
    $> $$;
Query OK, 0 rows affected (0.02 sec)

mysql> CALL test_catch_throw_signal();
Query OK, 0 rows affected (0.04 sec)

mysql> SELECT mle_session_state("stdout")\G
*************************** 1. row ***************************
org.graalvm.polyglot.nativeapi.PolyglotNativeAPI$CallbackException: SQL-CALLOUT: 
Error code: 1001 Error state: 45000 Error message: `Some error`

1 row in set (0.00 sec)

sql_state and error_number must be of type Number. MLE throws an exception if either of these values is Infinity or NaN.

You can also invoke SIGNAL from JavaScript routine code to throw an exception, similar to what is shown here:

mysql> CREATE PROCEDURE test_signal_no_catch() LANGUAGE JAVASCRIPT
    -> AS $$
    $>     console.clear()
    $>     session.runSql("SIGNAL SQLSTATE '45000' SET MESSAGE_TEXT= 'Some error', MYSQL_ERRNO = 1000")
    $> $$;
Query OK, 0 rows affected (0.01 sec)

mysql> CALL test_signal_no_catch();
ERROR 1000 (45000): Some error