The reason %save_hash changes is because you are copy a referance to an array. If you print out $hash{$a} you will see it contains a referance to an array, and that is what you are putting into $save_hash{$a}. You need to work your way down to copying the values, one way to do this is below:

sub save_state
{
 my %save_hash;

# foreach is your friend
foreach $key (keys (%main_hash)){
    foreach $num1 (0..$#{$main_hash{$key}}){
        foreach $num2 (0..$#{$main_hash{$key}[$num1]}){

# Now we are far enough down to copy the values
            $save_hash{$key}[$num1][$num2] = $main_hash{$key}[$num1][$
+num2];
        }
    }
}
 my @save_info;
 
 push(@save_info,\%save_hash);
 push(@save_info,\$aVar);
 # etc. for all vars to save
 
 push(@save_stack,\@save_info);
}
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I sure that you will soon get a list of 1001 moduals that do this better.