Is this on a post? Options? Taxonomy?
You need to build a CRON that looks at wherever the values are stored and checks the dates and then removes them if they are past.
For example if these fields are on some type of post then the cron needs to do a query that gets all of the posts that have values in this field, loops over those posts, checks the date and then updates or removes the field value.
https://developer.wordpress.org/plugins/cron/
