I fear that the only way that you can do what you want is to delete the Outlook database on your pc
Quite rightly, Microsoft view the PC as the main device in the partnership: the Axim is not a pc replacement so it will never clear all of the appointments and contacts on the host machine (only the other way round). Unless someone has a better solution, the only thing that I can suggest is a clean install of Outlook (including the database) and then resync. Backup to a card or your hdd first if you try this and I would also recommend creating a restore point and a full-backup of your data.