I have found what was delaying Mail. I have turned off TimeMachine and it seems to have solved the Mail issues. From what I understood the TimeMachine is creating snapshots of the system and when Mail is handling vast amount of emails (importing, moving between folders, etc) it "gets stuck" with the TimeMachine snapshots.
For me it solved the issues with Mail: go to TimeMachine, remove tick on "Back Up Automatically", delete the pending timeshots in the system (waiting the TimeMachine Volume to be connected) by using the Terminal. Restart the system. Start Mail and repeat the operation with emails (importing, moving between folders, etc).
After all emails organized then you can go back to TimeMachine and add again the tick on "Back Up Automatically".