How to show only one image in homepage

If I understand your question right, a function that truncates your text after stripping HTML is what you need.

What about using wp_trim_words():

<?php while($breakingnews->have_posts()) : $breakingnews->the_post(); ?>
    <a href="https://wordpress.stackexchange.com/questions/253344/<?php the_permalink(); ?>"><?php the_post_thumbnail('post-image'); ?></a>
    <div class="leadnewsboxtitle">
        <h2><a href="https://wordpress.stackexchange.com/questions/253344/<?php the_permalink(); ?>"><?php the_title(); ?></a></h2>
        <p><?php echo wp_trim_words( get_the_content(), 60, '...' ); ?></p>
    </div>
<?php endwhile; ?>

General usage:

wp_trim_words( string $text, int $num_words = 55, string $more = null )