stripping tags from excerpt in WordPress is not working

the_excerpt() automatically echoes the excerpt text. What you need is get_the_excerpt():

<a href="https://wordpress.stackexchange.com/questions/108530/<?php the_permalink() ?>" title="<?php echo strip_tags( get_the_excerpt() ); ?>">

However, it probably won’t strip out ellipses (…) since they’re HTML entities, not tags.