As already mentioned, the burning is done before the harvest.
Sugarcane is a grass and regrows and so can be harvested again without replanting (usually 3 years).
I used to live in a village North of Khon Kaen city and contractors from Korat and Kanchanaburi would collect locals to go and work for them. They were usually away from November until Songkran. Obviously these contractors had a lot of work and yet they chose to use manual labour. You would think that if anyone was going to use harvesting machines, it would be them. I guess there are reasons that they opted for the manual approach.