You can tell by the ID on the <link href="https://wordpress.stackexchange.com/questions/287569/... tag that the stylesheet”s ID is mesmerize-style, so you should be able to dequeue with this function in your child theme.
wp_dequeue_style( 'mesmerize-style' );
Make sure it’s hooked into wp_enqueue_scripts with a higher priority than the parent theme’s hook (probably 10).
That’s the general answer that would apply to most WordPress sites, and is a useful answer to the community, but since I’ve looked at your specific parent theme I can elaborate on your specific issue (which really should have originally been addressed to the author):
Your parent theme is loading its stylesheet in a weird way. It’s using get_stylesheet_uri(), which will load style.css from the theme, or from the child theme, if it exists. But it’s modifying it to load style.min.css, which you mustn’t have in your child theme. You could simply create an empty style.min.css to stop the 404, or you could dequeue the parent theme’s enqueue of the missing stylesheet, as above.