Replace multiple characters from string without using any nested replace functions

I believe it is easier and more readable if you use a table to drive this.

declare @String varchar(max) = '(N_100-(6858)*(6858)*N_100/0_2)%N_35'

--table containing values to be replaced
create table #Replace 
(
    StringToReplace varchar(100) not null primary key clustered
    ,ReplacementString varchar(100) not null    
)

insert into #Replace (StringToReplace, ReplacementString)
values ('+', '~')
    ,('-', '~')
    ,('*', '~')
    ,('/', '~')
    ,('%', '~')
    ,('(', '~')
    ,(')', '~')

select @String = replace(@String, StringToReplace, ReplacementString)
from #Replace a

select @String

drop table #Replace

There is not equivalent for the TRANSLATE function from Oracle in SQL Server, you have to use nested replace functions.

The following solution is technically correct:

DECLARE @newstring VARCHAR(100) = '(N_100-(6858)*(6858)*N_100/0_2)%N_35';
DECLARE @pattern VARCHAR(100) = '%[+-\*/%()]%';
DECLARE @i INT;
BEGIN
  SET @i = PATINDEX(@pattern,@newstring) 
  WHILE @i <> 0
  BEGIN
    SET @newstring = LEFT(@newstring,@i-1) + '~' + SUBSTRING(@newstring,@i+1,100);
    SET @i = PATINDEX(@pattern,@newstring) 
  END
  SELECT @newstring;
END;

But I do not see why you would favor this over nested REPLACE calls.