Remove all non-numeric characters from a field

There isn't any "builtin" function that will do this operation in MySQL.

One option is to create your own stored function (if you have sufficient privileges on the database).

 DELIMITER $$

 DROP FUNCTION IF EXISTS `uf_only_digits`$$

 CREATE FUNCTION `uf_only_digits`(as_val VARCHAR(65535))
 RETURNS VARCHAR(65535)
 DETERMINISTIC
 BEGIN
   DECLARE retval VARCHAR(65535);
   DECLARE i INT;
   DECLARE strlen INT;
   -- shortcut exit for special cases
   IF as_val IS NULL OR as_val = '' THEN
     RETURN as_val;
   END IF;
   -- initialize for loop
   SET retval = '';
   SET i = 1;
   SET strlen = CHAR_LENGTH(as_val);
 do_loop:
   LOOP
     IF i > strlen THEN
       LEAVE do_loop;
     END IF;
     IF SUBSTR(as_val,i,1) IN ('0','1','2','3','4','5','6','7','8','9') THEN
       SET retval = CONCAT(retval,SUBSTR(as_val,i,1));
     END IF;
     SET i = i + 1;
   END LOOP do_loop;
   RETURN retval;
 END$$

 DELIMITER ;

And be sure to test this before you use it an UPDATE statement.

 SELECT t.foo
      , uf_only_digits(t.foo)
   FROM ( SELECT '' AS foo
          UNION ALL SELECT ' x'
          UNION ALL SELECT 'a1b2'
          UNION ALL SELECT '1-888-555-1212 ext 213'
          UNION ALL SELECT '1-800-FLOWERS'
        ) t

Returns:

 foo                     uf_only_digits(t.foo)  newlen  
 ----------------------  ---------------------  --------
                                                       0
  x                                                    0
 a1b2                    12                            2
 1-888-555-1212 ext 213  18885551212213               14
 1-800-FLOWERS           1800                          4

(The last two rows might give us pause to reconsider what we really want to achieve. If it were me, I would creating a new column, and saving the existing value in it, before I did an UPDATE.)

 -- new column same size as `phone` column
 ALTER TABLE mytable ADD COLUMN orig_phone VARCHAR(40) NULL 
   COMMENT 'original phone value, before update to all digits';

 UPDATE mytable t
    SET t.orig_phone = t.phone ;

 UPDATE mytable t
    SET t.phone = uf_only_digits(t.phone) ;

This may work but little tedious:

Get the list of number from the table

$result = mysql_query("Select ID, number from Table"); 

On each value

while ($row = mysql_fetch_array($result)) { 
$ID = $row["ID"]; 
$NUM = $row["number"]; 

Then do a regex pattern and update that value to the ID

$NUM = eregi_replace("whateverregex","",$NUM); 

$sql = mysql_query("Update Table set number = $NUM where ID = $ID"); 
} 

On MySQL 8.0+ there is a new native function called REGEXP_REPLACE. A clean solution to this question would be:

update table set data = REGEXP_REPLACE(data, '[^0-9]+', "") where condition

It's not pretty, but...

UPDATE table
SET data =
 CONCAT(
    IF (SUBSTRING(data, 01, 1) REGEXP '[0-9]', SUBSTRING(data, 01, 1), '')
,   IF (SUBSTRING(data, 02, 1) REGEXP '[0-9]', SUBSTRING(data, 02, 1), '')
,   IF (SUBSTRING(data, 03, 1) REGEXP '[0-9]', SUBSTRING(data, 03, 1), '')
,   IF (SUBSTRING(data, 04, 1) REGEXP '[0-9]', SUBSTRING(data, 04, 1), '')
,   IF (SUBSTRING(data, 05, 1) REGEXP '[0-9]', SUBSTRING(data, 05, 1), '')
,   IF (SUBSTRING(data, 06, 1) REGEXP '[0-9]', SUBSTRING(data, 06, 1), '')
,   IF (SUBSTRING(data, 07, 1) REGEXP '[0-9]', SUBSTRING(data, 07, 1), '')
,   IF (SUBSTRING(data, 08, 1) REGEXP '[0-9]', SUBSTRING(data, 08, 1), '')
,   IF (SUBSTRING(data, 09, 1) REGEXP '[0-9]', SUBSTRING(data, 09, 1), '')
,   IF (SUBSTRING(data, 10, 1) REGEXP '[0-9]', SUBSTRING(data, 10, 1), '')
,   IF (SUBSTRING(data, 11, 1) REGEXP '[0-9]', SUBSTRING(data, 11, 1), '')
,   IF (SUBSTRING(data, 12, 1) REGEXP '[0-9]', SUBSTRING(data, 12, 1), '')
,   IF (SUBSTRING(data, 13, 1) REGEXP '[0-9]', SUBSTRING(data, 13, 1), '')
,   IF (SUBSTRING(data, 14, 1) REGEXP '[0-9]', SUBSTRING(data, 14, 1), '')
,   IF (SUBSTRING(data, 15, 1) REGEXP '[0-9]', SUBSTRING(data, 15, 1), '')
,   IF (SUBSTRING(data, 16, 1) REGEXP '[0-9]', SUBSTRING(data, 16, 1), '')
)
WHERE condition

You may have to duplicate the concatenated IF function more times depending on the length of field and how much formatting was entered.

See the query in action at SQLFiddle