Easy way to show excerpts of specific posts on a page

You need a couple of things. A shortcode handler, and a custom query:

function wpse_186346_excerpt_length() {
    return 50;
}

function wpse_186346_excerpt( $atts ) { 
    $atts = wp_parse_args( $atts,
        array(
            'posts_per_page' => 2,
            // Any other default arguments
        )
    );

    // We don't need paging, always save a query
    $atts['no_found_rows'] = true;

    // Create query based off arguments from shortcode  
    $query = new WP_Query( $atts );

    // Start the buffer to "catch" our output below, so that we can return it as a string
    ob_start();

    // Set our custom excerpt length
    add_filter( 'excerpt_length', 'wpse_186346_excerpt_length' );

    // Loop over the posts and output whatever markup you need
    while ( $query->have_posts() ) {
        $query->the_post();
        the_title( '<h4 class="excerpt-title"><a href="' . get_permalink() . '">', '</a></h4>' );
        the_excerpt();  
    }

    // Remove our custom excerpt length
    remove_filter( 'excerpt_length', 'wpse_186346_excerpt_length' );

    // Restore the current global post
    wp_reset_postdata();

    return ob_get_clean();  
}

add_shortcode( 'excerpt', 'wpse_186346_excerpt' );

And use it like so:

[excerpt tag="test_tag"]

Your shortcode arguments just need to match those available, so you’re not limited to only tags!