Clear missing index DMVs
No, there is no knob for clearing just missing_index DMVs. You'll have to restart the service or, if you want to exclude specific tables, you could create a view against the DMVs with a filter.

The only DMVs you can clear manually, using DBCC SQLPERF, are sys.dm_os_wait_stats and sys.dm_os_latch_stats:


DBCC SQLPERF 
(
     [ LOGSPACE ]
     |
          [ "sys.dm_os_latch_stats" , CLEAR ]
     |
     [ "sys.dm_os_wait_stats" , CLEAR ]
) 
     [WITH NO_INFOMSGS ]