Suggestions:

1. To avoid the IO overhead of creating, then reading the file (which, presumably you do not need for other purposes),
you can pipe the command output directly into a perl filehandle using a construct like:

open(my $netbackup, "-|", "autorep -J NB\%") or die could not open net
+backup:$!";
while (<$netbackup>){
  next if m/Job Name|____/;
  # do the equivalent of sed
  #Presumably, you don't need sort 
  # If you do, you can apply filters, accumulate, THEN sort in perl.
}
close $netbackup;
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2. Since you have already read in @server_names, you can grep each of those to find if any are in the line read from $netbackup, and process it.