Exclude specific taxonomy term when using wp_get_post_terms

I’d use wp_list_filter() with the operator ‘NOT’ to compare either the term’s name, slug or ID (depending how you want to test for term to be exluded).

Untested but something like this should work (assuming that you want to exclude the term with slug ‘myslug’):

 $terms = wp_get_post_terms( $post->ID, 'wedding_cat');
 $terms = wp_list_filter($terms, array('slug'=>'myslug'),'NOT');

(Of course this may mean $terms because empty).