Found a solution (probably not the best way to do this)…
[ Moderator Note: Please post code or markup snippets between backticks or use the code button. ]
<!-- Start Counting Loop -->
<?php
$args = array(
'post_type' => 'puppies',
'taxonomy' => 'litter-type',
'term' => 'previous-litters',
'posts_per_page' =>-1
);
$loop = new WP_Query($args);
if ( $loop->have_posts() ) : ?>
<?php
while ( $loop->have_posts() ) : $loop->the_post(); ?>
<?php $amt = get_post_meta($post->ID, 'wpcf-litter-puppies', true);?>
<?php if ($amt) {$previous_puppies_total += $amt;};?>
echo $total; ?>
<?php endwhile; ?>
<?php echo 'Puppies from previous litters: '.$previous_puppies_total; ?>
<?php endif; ?>
<?php wp_reset_postdata(); ?>
<!-- End Counting Loop -->