This is a tricky one.
'crontab' has a limited environment, included a very short path. Although 'service' is on this very basic path, 'service' is actually an script that that calls other scripts.
start, stop and status are not real parameters, but other programs that live on /sbin, which is not in the limited crontab path.
You can check it yourself by doing:
The easy solution then, is to expand the path as the first line of your crontab, so that includes /sbin. For instance:
$ ls /sbin/stop /sbin/start /sbin/status
/sbin/start /sbin/status /sbin/stop
I hope that helps, and let us know how it goes.
# m h dom mon dow command
*/1 * * * * service mysql stop