You know that your usage is ok, so there's no objection to just turning off the warning. I'll show a trick for eliminating some temporary variables, too.

my @substrings;
{
    my $size = 10;
    no warnings 'substr';
    push @substrings, substr($string, 0, $size, '')
        while $string;
}
[download]

If you want nondestructive treatment of $string, you can make a copy inside the curlies and work on that.

Update: Here's yet another way to do it in 5.8+,

my @substrings = do {
    local $/ = \10;
    open my $fh, '<', \$string;
    <$fh>
};
[download]