Mark certainly has a good point about meeting the criteria for ADHD. An important part of the DSM 5 criteria is that the symptoms have lasted for at least 6 months and that they occur in at least two places. Besides reading Marks excellent link, you might also want to check this one out.
The fact that a 6 year old is being sent to the Principals office and that he has had his teacher in tears would suggest that the discipline that the school has been trying is also not effective.
I do think that it is time to get him evaluated by a mental health professional. If he does have ADHD there are many non-medical things that can be done by both you and the school.
School wise a 504 plan will become very important. I can get you more information on that if it is needed.
On the ADHD forum - http://www.medhelp.org/forums/ADD---ADHD/show/175 -
where I am also the CL I recently posted some links on discipline, etc (and I have many more) which you might find helpful.
Hope this helps. Please post here or over on the ADHD forum if you have any more questions. Best wishes.