MySQL shouldn't crash because of queries like those, but it could feel like it does because your site won't work.
I'd first run
SELECT option_name, length(option_value) FROM wp_options WHERE autoload = 'yes' ORDER BY length(option_value) DESC;
to see if some option has accumulated a large value (I've seen wp-cron entries grow very large in one release ~2 years back).
Also check how many options will be automatically loaded:
SELECT count(*) FROM wp_options WHERE autoload = 'yes';
Those are usually a few hundred, if it's a very large number, investigate further.
If both these queries don't show anything weird, you may want to look into MySQL itself. Is the RAM on your machine exhausted and (slow) SWAP is being used? Is there a faulty hard disk and re-reads are timing out?