Using SQL REPLACE where the replaced string and replacement are the result of another replacement

For no more then 2 replacements

SELECT t2.col2, REPLACE(REPLACE(t2.col2,t1.col1,REPLACE(t1.col1, '-', '_')),t3.col1,REPLACE(t3.col1, '-', '_')) 
FROM table_2 t2
JOIN table_1 t1 ON t2.col2 like '%' +t1.col1+'%' AND t1.col1 LIKE '%-%'
LEFT JOIN table_1 t3 ON t3.col1 <> t1.col1 AND t2.col2 LIKE '%'+t3.col1+'%' AND t3.col1 LIKE '%-%'
WHERE t2.col2 LIKE '%-%'

This is fully ad-hoc, no recursion needed:

DECLARE @table_1 TABLE(ID INT IDENTITY,col1 VARCHAR(100));
INSERT INTO @table_1 VALUES    
 ('string-1'),('string-2'),('string-3');

DECLARE @table_2 TABLE(ID INT IDENTITY,col1 VARCHAR(100));
INSERT INTO @table_2 VALUES    
 ('text string-1 text string-3'),('text string-3 string-2 t-ext'),('string-2 text string-3 te-xt');

--The first CTE replaces the value in t1

WITH t1New AS
(
    SELECT ID AS t1_ID
          ,t1.col1 AS t1c1
          ,REPLACE(t1.col1,'-','_') AS new_t1c1 
    FROM @table_1 AS t1
)

--The second CTE splits the strings of t2 on the blanks

,t2Splitted AS
(
    SELECT ID
          ,col1 AS t2c1
          ,CAST('<x>' + REPLACE(t2.col1,' ','</x><x>') + '</x>' AS XML) AS Casted
    FROM @table_2 AS t2
)

--This CTE maps the values to the splitted parts

,Mapped AS
(
    SELECT t1New.*
          ,t2Splitted.ID AS t2_ID 
          ,ROW_NUMBER() OVER(PARTITION BY t2Splitted.ID ORDER BY (SELECT NULL)) AS PartIndex
          ,part.value('.','nvarchar(max)') AS Part
    FROM t2Splitted
    CROSS APPLY t2Splitted.Casted.nodes('/x') AS A(part)
    LEFT JOIN t1New ON t1New.t1c1=part.value('.','nvarchar(max)')
)

--If there is a mapping, the new value is taken, else take the old value

,NewValues AS
(
    SELECT *
           ,CASE WHEN t1c1 IS NOT NULL THEN new_t1c1 ELSE Part END AS newValue
    FROM Mapped 
)

--The final CTE re-concatenates the string with blanks in the original order

,Final AS
(
    SELECT nv1.t2_ID
      ,(SELECT ' ' + nv2.newValue
        FROM NewValues AS nv2
        WHERE nv2.t2_ID=nv1.t2_ID
        ORDER BY PartIndex
        FOR XML PATH('')) AS FinalValue
    FROM NewValues AS nv1
    GROUP BY nv1.t2_ID
)

--This last value is used to update the original table

UPDATE t2 SET t2.col1=Final.FinalValue
FROM @table_2 AS t2
INNER JOIN Final ON Final.t2_ID=t2.ID

What's up to you: UPDATE t1, that's a one-liner and get rid of the trailing space in FinalValue :-)

SELECT * FROM @table_2

Variable based replacement can be done as replacing with a table.

DECLARE @Raw NVARCHAR(MAX) = '...';
SELECT @Raw= REPLACE(@Raw, P, R)
FROM (VALUES ('string-1', 'string_1'),
            ('string-2','string_2'),
            ('string-3','string_3'),
            ('string-4','string_4'),
) AS T(P, R);

To execute the same logic against table, think about some statements like

SELECT col1, MultipleReplace(col1, replacement_table(P, R))
FROM some_table

So create a function that accepts a string input and a replacement table. In order to pass table to function, we have to create a table type.

CREATE TYPE dbo.MulReplacements AS TABLE 
(
    Pattern NVARCHAR(MAX) NOT NULL,
    Replacement NVARCHAR(MAX) NOT NULL
)

Then the function would be

CREATE FUNCTION dbo.MulReplace(
    @string AS NVARCHAR(MAX),
    @replacements AS dbo.MulReplacements READONLY
)
RETURNS NVARCHAR(MAX)
AS
BEGIN
    DECLARE @result AS NVARCHAR(MAX) = @string;

    SELECT @result = REPLACE(@result, R.Pattern, R.Replacement) 
    FROM @replacements AS R;

    RETURN @result;
END

Put all together

DECLARE @replacement AS dbo.MulReplacements;

INSERT INTO @replacement
SELECT col1, REPLACE(col1, '-', '_')
FROM (VALUES ('string-1'), ('string-2'), ('string-3')) AS table_1(col1)

SELECT col1, dbo.Mulreplace(col1, @replacement)
FROM (VALUES ('text string-1 text string-3'), ('text string-3 string-2 t-ext'), ('string-2 text string-3 te-xt')) AS table_2(col1)

One way of doing it with Dynamic query. Replace the actual table name and column names (commented where to change).

DECLARE @colNames VARCHAR(MAX) = ''
SELECT @colNames = @colNames + ', [' + table1_Col1 + ']' FROM tableName1 -- Table1 Column and Table1 Name
DECLARE @ReqColNames VARCHAR(MAX) = STUFF(@colNames, 1, 1, '')

DECLARE @int int
SELECT @int = count(*) FROM tableName1 -- Table1 Name
DECLARE @replace varchar(max) = replicate('REPLACE(', @int) + 't2.table2_Col2' -- Table2 Column

DECLARE @replaceCols varchar(max) = ''
SELECT @replaceCols = @replaceCols + ', r.[' + table1_Col1 + '], replace(r.[' + table1_Col1 + '], ''-'', ''_''))' FROM tableName1 -- Table1 Column and Table1 Name
DECLARE @ReplaceString varchar(max) = @replace + @replaceCols


DECLARE @cmd varchar(max) = 'SELECT ' +  @ReplaceString + ' FROM
(
    SELECT * FROM tableName1
    PIVOT
    (MAX (table1_Col1) FOR table1_Col1 IN (' + @ReqColNames + ')) x
) r
CROSS JOIN tableName2 t2'

EXEC(@cmd)

Static Query: for above code (to show what the above dynamic code is generating):

Select replace(replace(replace(t2.table2_Col2
        , r.[string-1], replace(r.[string-1], '-', '_'))
        , r.[string-2], replace(r.[string-2], '-', '_'))
        , r.[string-3], replace(r.[string-3], '-', '_'))
from
(
    Select * from tableName1
    PIVOT
    (MAX (table1_Col1) FOR table1_Col1 IN ([string-1], [string-2], [string-3])) x
) r
CROSS JOIN tableName2 t2

Output:

text string_1 text string_3
text string_3 string_2 t-ext
string_2 text string_3 te-xt