There is no such thing as computed column in MySQL.
If you want to format some value to speed-up index search, you will probably have to use some trigger. As a matter of fact, I answered almost the same question this morning: see https://stackoverflow.com/a/18047511/2363712 for a similar example.
In your case, that would lead to something like that:
CREATE TABLE `table_a`(`column_1` VARCHAR(255), ... ,
`column_1_fmt` VARCHAR(255),
INDEX(`column_1_fmt`));
CREATE TRIGGER ins_table_a BEFORE INSERT ON `table_a`
FOR EACH ROW
SET NEW.`column_1_fmt` = REPLACE(NEW.column_1, '-', '');
CREATE TRIGGER upd_table_a BEFORE UPDATE ON `table_a`
FOR EACH ROW
SET NEW.`column_1_fmt` = REPLACE(NEW.column_1, '-', '');
Now you will use column_1_fmt
to search for values/join on values having the required format.
Concerning your special need (removing dashes -- from some kind of serial/reference number?). Maybe you should reverse the problem. Store those value as canonical form (no dash). And add required dashes at SELECT
time.