Short answer--don't slurp the entire file.

Longer answer. If the text you are removing extends across multiple lines, you may be able to use paragraph mode ($/ = ' ';) to effect processing the file in smaller chunks.

If not, then you will need to use something like the sliding buffer technque demonstrated in Re: split and sysread() and towards the end of Optimising processing for large data files..

There are also other discussions of the "sliding buffer" technique on this site--try a super search for that term.