I would also advise using established modules for this, but here's another regex-only way to remove the first n directories from an absolute path. It looks like you're using a *nix path, and I haven't made the effort to define a proper directory pattern in  $dir (I don't think that any character other than a  / is allowed), so you will have to fix up the  [^/] character class accordingly.

c:\@Work\Perl\monks>perl -wMstrict -le
"my $filespec = '/usr/share/directory/piano_book.mp4';
 print qq{absolute: '$filespec'};
 ;;
 my $dir = qr{ / [^/]+ }xms;  # fix [^/]
 ;;
 my $n = 2;
 die qq{'$filespec' could not be made relative}
   unless $filespec =~ s{ \A (?: $dir){$n} }{.}xms;
 print qq{relative: '$filespec'};
"
absolute: '/usr/share/directory/piano_book.mp4'
relative: './directory/piano_book.mp4'
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Please see perlre, perlretut, and perlrequick.

Update: Added error check to substitution in example code.