You sure can. amaysim customers stay because they want to, not because they have to.
If you're transferring your amaysim number to a different Aussie telco, simply contact them to arrange the transfer. Your new provider will then touch base with us to organise the transfer and cancellation of your amaysim service.
If you're not transferring your amaysim number, just contact us on Live Chat (or via email if out of hours). Just a heads up that you would lose your amaysim mobile number, along with any unused amaysim credit and/or data and any saved voicemails. If you want to use amaysim again in the future, you'd simply need to buy a new SIM.