#!/usr/bin/perl

use strict;
use warnings;
use autodie;

if (@ARGV != 1){
    print "USAGE: ./parse-counts.pl file\n";
    exit(1);
}

my $mutfile = $ARGV[0];
open(INPUTR,"<$mutfile") or die "Can't open \$mutfile for reading. \n";

my (%counts, %unique, %masks);
my ($headname, @unique) = grep !$unique{$_}++, my @headers = split /\t/, <INPUTR>;

# the basic syntax is @out = map { CODE } @in;

for my $label ( @unique )
{
    $masks{$label} = join "\t",
    map { $_ eq $label ? 'MUTS' : '_' } @headers[1..$#headers];
}

my $line;

while($line=<INPUTR>)
#while(<DATA>)
{
    chomp $line;
    $line =~ s/\t/\t/g; # for uniform spacing
    my ($name, $letters) = split /\t/, $line, 2;
    $counts{$name}{$_} += ($masks{$_} | $letters) =~ /MUTS/ for @unique;
    print $name."\n";
    print $letters."\n";
}

print "$headname @unique\n";
print "$_ @{ $counts{$_} }{@unique}\n" for sort keys %counts;


The output produced is:
Gname G1 G2 G3

A 3 2 0
B 2 1 1
C 2 0 0

The modified datafiles is
Gname   G1      G1      G1      G1      G2      G2      G3
A       W       W       MUTS    W       W       W       MUTS
A       W       W       W       W       W       W       W
A       W       W       W       W       W       W       W
B       W       W       W       W       W       MUTS    MUTS
B       MUTS    W       W       W       W       MUTS    MUTS
C       MUTS    MUTS    MUTS    W       W       W       W
C       MUTS    W       W       MUTS    MUTS    W       W