This sooo looks like homework. Oh, well.

You'll probably be interested in the s modifier for regex matching. (See perlre for more detail.):

#!/usr/bin/perl
use strict;
use warnings;

my $poem;

{
        local $/ = undef;
        $poem = <DATA>;
}

my( $before, $after) = $poem =~ m/(.*)\bDOG\b(.*)/s;

print "Text before:\n$before\n\n";
print "Text after:\n$after\n\n";

__DATA__
A Beautiful Poem
Mary had a little lamb, little lamb, little lamb
Mary had a DOG but everywhere that mary went the lamb was
sure to go even though it did not like the dog very much.


# Output

Text before:
A Beautiful Poem
Mary had a little lamb, little lamb, little lamb
Mary had a

Text after:
 but everywhere that mary went the lamb was
sure to go even though it did not like the dog very much.
[download]