How about returning up front? Say for example, if monster.pl contains:

#!/usr/bin/perl

sub mysub {print "I want to see this\n"};

print "but I don't want to see this\n";

exit;  # don't want to exit either
[download]

Then:

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

my $prog_code = do {local $/ = undef;
            open (my $fh, '<', 'monster.pl')
            or die "open error: $!";
            <$fh>};

eval 'return;'.$prog_code ;
die "eval error: $@" if $@; 

warn "trying mysub";
mysub();
[download]

The return gets executed as soon as compilation has finished, avoiding execution of the main body:

perl do.pl
trying mysub at do.pl line 13.
I want to see this
Compilation finished at Wed Aug  4 10:08:26
[download]

Update: Removed intermediate subroutine and added sample output.