First, start by defining a CGI object. Now the rest of the param and form element references in the script should be edited accordingingly with a $query->. Next move the data handling code to the top of your script and simply execute a $query->delete_all(); when you are done with it. This will clear your form data before it is printed again.

Kinda like this:

#!/usr/bin/perl

use CGI qw/:standard/;
$query= new CGI;
if ($query->param()) {
        open (CFGFILE,">>mothership.cfg") || die;
        print CFGFILE (param('name')),",",
        ($query->param('ip')),",",
        ($query->param('port')),",",
        ($query->param('proto')),",",
        ($query->param('desc')),
        "\n";
        close CFGFILE;
        $query->delete_all();
}

print header,
start_html('Mothership Connection'),
h1('Mothership Connection Configuration'),
        $query->start_form,
        "Server Name ",$query->textfield('name'),p,
        "IP Address ",$query->textfield('ip'),p,
        "Port Number",$query->textfield('port'),p,
        $query->checkbox_group(-name=>'proto',
                       -values=>['tcp','udp']),p,
        "Description",$query->textfield('desc'),p,
        $query->submit('submit'),
        $query->end_form,
hr;
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