List minutes instead of grouping by them
You can use the timestampdiff function. You need to use the start date as a second argument, like this:

SELECT TIMESTAMPDIFF(MINUTE,'2014-06-12 10:00:00', timestamp) AS mins, 
COUNT(field) 
FROM table 
WHERE timestamp BETWEEN '2014-06-12 10:00:00' AND '2014-06-12 12:00:00' GROUP BY mins;