There is more than one way to do it:

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

my @data = ('RRsnap02  2013-07-24 12:35:35',
            'vmk000    2013-07-22 17:16:50',
            'vmk001    2013-07-22 20:00:36',
            'vmk009    2013-07-23 18:21:12',
            'vmk010    2013-07-23 18:31:00',
            'vmk020    2013-07-23 23:30:43',
            'vmk024    2013-07-24 03:27:30',
            'vmk031    2013-07-24 10:27:36',
            'vmk032    2013-07-24 11:27:38',
            'vmk032    2013-07-24 11:27:38',
           );


sub get_date {
    my $s = shift;
    $s =~ s/^\S+\s+//;
    return $s;
}

# Simple:
print "$_\n" for sort { get_date($a) cmp get_date($b) } @data;

# Faster, Schwartzian transform, computes get_date just once for each 
+line:
print "$_\n" for map  $_->[1],
                 sort { $a->[0] cmp $b->[0] }
                 map  [ get_date($_), $_ ],
                 @data;

# Orcish maneuver, compute get_date only when needed and cache:
my %cache;
print "$_\n" for sort {
                     ( $cache{$a} //= get_date($a) )
                       cmp
                     ( $cache{$b} //= get_date($b) )
                 } @data;

# Guttman Rosler Transform, changing to strings for default sort:
print "$_\n" for map { s/(.*) (\S+\s+)$/$2$1/; $_ }
                 sort
                 map { s/^(\S+\s+)(.*)/$2 $1/; $_ }
                 @data;
[download]

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