Removing the […] from the excerpt returned by get_the_excerpt() only in some places

Don’t use get_the_excerpt. Just do something like:

if (is_singular() && isset($post->post_excerpt)) {
    echo '<meta name="description" content="'.esc_attr($post->post_excerpt).'" />';
}

$post is populated long before the Loop. For “single” pages it will be populated with the post to be displayed. You can grab it very early in the page load. For other types of pages– archives, capital “P” Pages– it may not have the value you expect, so watch it.

Caveats:

1. That assumes that your posts all have actual excerpts. Nothing will be auto-generated from post content.
2. I have no idea how you theme works. You may need to edit a theme file. You may need to build a function and hook it to a theme hook or to wp_head.