How to setting up the custom size thumbnail for wp_get_attachment_thumb_url()?

I meant you should use wp_get_attachment_image_src() with your $cat_thumb_id. Try this:

$cat_thumb_id  = get_woocommerce_term_meta($cat->term_id, 'thumbnail_id', true);
$cat_thumb     = wp_get_attachment_image_src($cat_thumb_id, 'medium_large');
$cat_thumb_src = $cat_thumb[0] ? esc_url($cat_thumb[0]) : mytheme_catch_that_image();

?><img src="https://wordpress.stackexchange.com/questions/226005/<?php echo $cat_thumb_src; ?>" alt="<?php echo $cat->name; ?>"/>