Replace value using several criteria in another table
Creating the schema - Tables that will be used for the example:

DECLARE @table_1 TABLE (
    someText VARCHAR(10)
)
INSERT INTO @table_1 values ('abcdefghij')
INSERT INTO @table_1 values ('fajiefhda')
INSERT INTO @table_1 values ('hurineajsd')

DECLARE @table_2 TABLE (
    value VARCHAR(10)
)
INSERT INTO @table_2 values ('d')
INSERT INTO @table_2 values ('f')
INSERT INTO @table_2 values ('h');


Procedural code starts here. First a temporary table is used to get the replace strings numbered so we can iterate on them:

DECLARE @table_2_numbered TABLE (
    RowNum int,
    value VARCHAR(10)
);

INSERT INTO @table_2_numbered
SELECT ROW_NUMBER() OVER (ORDER BY value ASC) AS RowNum, value
FROM @table_2;


The following CTE will pick up the original strings that we want to update (@table_1) and will iterate through each row of the table with the replacing strings, which are now numbered (@table_2_numbered), and recursively apply them to replace every desired occurence. Notice we keep track of the original strings so we know which replaced strings correspond to which original strings:

WITH CTE (originalText, replaced, iteration)
AS
(
    SELECT someText AS originalText
        , someText AS replaced
        , 1 AS iteration
    FROM @table_1 t1
    UNION ALL
    SELECT CTE.originalText
        , CAST(REPLACE(CTE.replaced, value, '') AS VARCHAR(10)) AS replaced
        , iteration + 1 AS iteration
    FROM CTE, @table_2_numbered t2
    WHERE t2.RowNum = iteration
)
UPDATE t1 SET t1.someText = CTE.replaced
FROM @table_1 t1, CTE
WHERE CTE.iteration = (SELECT MAX(RowNum)+1 FROM @table_2_numbered)
    AND t1.someText = CTE.originalText

SELECT * FROM @table_1


And here are the results:

someText
--------
abcegij
ajiea
urineajs