Grygonos,
If your goal is to delete a specific character and you want to do it through your entire string - it would probably be better to use tr.

$row[0] =~ tr /\///d;
[download]

To answer the question you asked - you would need to add the g modifier to make the substitution global and to make it a null, you would make the subsitution empty:

$row[0] =~ s/\///g;
[download]

You may also want to check out changing your delimiters so that you avoid the "leaning toothpick" syndrome.

Cheers - L~R