Sort records based on "status" field value (running, upcoming, closed) and the records should come based on date in mysql

First use ROW_NUMBER() window function to rank the rows of each status and then check the value of each status:

SELECT *
FROM tablename
ORDER BY ROW_NUMBER() OVER (PARTITION BY status ORDER BY date, time), 
         status = 'running' DESC,
         status = 'upcoming' DESC,
         status = 'closed' DESC;

If your version of MySql does not support window functions use a correlated subquery:

SELECT t1.*
FROM tablename t1
ORDER BY (
           SELECT COUNT(*) 
           FROM tablename t2 
           WHERE t2.status = t1.status 
             AND CONCAT(t2.date, t2.time) <= CONCAT(t1.date, t1.time)
         ), 
         status = 'running' DESC,
         status = 'upcoming' DESC,
         status = 'closed' DESC;

See the demo.