Help using REPLACE with wildcard matching pattern....

OK just for fun, here's a TSQL method, using Jeff Moden's Tally table, and a SQL2005 (and later) trick for concatenating the results back

--Jeff Moden Tally table
    if object_id('dbo.tally') is not null 
    drop table dbo.tally

    select top 10000 --change to fit max lenght of phone number
            identity(int,1,1) as n
       into dbo.tally
       from master.dbo.syscolumns sc1,
            master.dbo.syscolumns sc2

    -- add pk to maximize performance
      alter table dbo.tally
        add constraint pk_tally_n 
            primary key clustered (n) with fillfactor = 100

declare @phonetable table 
        (uniqueid int identity(1,1), phone_number varchar(500))
insert into @phonetable (phone_number)
        select '01234-567-890'
union   select '012345 6789ext' 
union   select 'n/a'
union   select '...12345.....'

;with cte (uniqueid, phone_number, goodchar, badchar) as(
select
    uniqueid, phone_number, 
    case when substring(phone_number,N,1) not like '%[^0-9]%' 
         then substring(phone_number,N,1) end as goodchar,
    case when substring(phone_number,N,1) like '%[^0-9]%' 
         then substring(phone_number,N,1) end as badchar

from @phonetable , Tally
where phone_number like '%[^0-9]%'
and N <= len(phone_number)
)

SELECT distinct
        phone_number,
        isnull(
        stuff ( ( SELECT
                          '' + goodchar
                  FROM
                          cte t1
                  where t1.UniqueID = t2.UniqueID
        FOR XML PATH ( '' ) ) , 1 , 0 , '' )
        ,'') as clean_phone_number
from cte t2

gives

phone_number        clean_phone_number
...12345.....        12345
012345 6789ext       0123456789
01234-567-890        01234567890
n/a 

CREATE FUNCTION ExtractInteger ( @String VARCHAR(2000) )
RETURNS VARCHAR(1000)
AS BEGIN 
    DECLARE @Count INT 
    DECLARE @IntNumbers VARCHAR(1000) 
    SET @Count = 0 
    SET @IntNumbers = '' 
    WHILE @Count <= LEN(@String) 
        BEGIN 
            IF SUBSTRING(@String, @Count, 1) >= '0'
                AND SUBSTRING(@String, @Count, 1) <= '9' 
                BEGIN 
                    SET @IntNumbers = @IntNumbers + SUBSTRING(@String, @Count, 1) 
                END 
            SET @Count = @Count + 1 
        END 


    RETURN @IntNumbers 

   END


-- SELECT dbo.ExtractInteger('0323-111-CALL')
-- gives  0323111

Why not?

Select (Replace(Replace(phone_number, '-', ''), ' ', '') from phone_table

Do you have a lot of different non-numeric characters? If not I would simply go for

USE [adventureworks]
GO    

SELECT phone, REPLACE([c].[Phone],'-','') 
FROM [Person].[Contact] AS c

if there are lots of different ones and you need to repeat this process regularly then you might need to get involved with regex, functions and even clr ...

DECLARE  @s      VARCHAR(1000), 
         @i      TINYINT, 
         @result VARCHAR(50) 

SELECT @s = '012345 6789ext' 

SET @i = 1 

SET @result = '' 

WHILE (@i <= Datalength(@s)) 
  BEGIN 
    SET @result = @result + Substring(@s,Patindex('%[0-9]%',@s),1) 

    SET @s = Stuff(@s,Patindex('%[0-9]%',@s),1,'') 

    SET @i = @i + 1 
  END 

SELECT @result