MySQL Tuning and optimization
[!!] Total fragmented tables: 551  -- bogus, ignore it
[0.071 qps],  -- very lightly loaded
[!!] Maximum possible memory usage: 126.3G (100% of installed RAM)  -- bogus, ignore it
[OK] Highest usage of available connections: 0% (2/600)  -- consider lowering max_connections
[OK] Key buffer size / total MyISAM indexes: 1.0G/153.6M  -- lower key_buffer_size
[!!] Query cache efficiency: 0.0% (0 cached / 3K selects)  -- Turn the QC off
[OK] Sorts requiring temporary tables: 5% (7 temp sorts / 125 sorts)  -- Let's see some slow queries and help you optimize them
[!!] Joins performed without indexes: 252  -- ditto
[OK] Temporary tables created on disk: 21% (344 on disk / 1K total)  -- ditto
[OK] Open file limit used: 0% (48/20K)  -- 20K?
[!!] InnoDB data size / buffer pool: 108.0G/107.0G  -- bogus; it's a cache!

General recommendations:
    Run OPTIMIZE TABLE to defragment tables for better performance  -- NO!
    MySQL started within last 24 hours - recommendations may be inaccurate  -- true
Variables to adjust:
  *** MySQL's maximum memory usage is dangerously high ***  -- bogus
  *** Add RAM before increasing MySQL buffer variables ***
    query_cache_limit (&gt; 1M, or use smaller result sets)  -- no, set to 0
    innodb_buffer_pool_size (&gt;= 107G)  -- No, it is dangerously high now (assuming you have 128GB of RAM)


For more analysis, provide SHOW VARIABLES and SHOW GLOBAL STATUS, plus RAM size.  (Due to limitations here, you may need a postit site.)

The biggest problem seems to be poorly designed/indexed queries.  Those cannot be fixed by tuning.