Removing this is not necessarily a problem w/asbestos unless you make it one.
By using a saw, you heat up the glue and it vaporizes and of course, creates dust. If it's inhaled in sufficient quantites, you put yourself at risk for at least a coughing bout, a bronchial bout, or the like. So, depending on 'how' you go about removing the floor, you may or may not put yourself at risk. Some folks recommend that you simply cover over the old flooring due to the hazard. I don't take that position because many states are in the process of mandating (or already mandated) that if you know of asbestos in the house, you have to disclose it when you go to sell the home. Knowing so, and not telling, and being PROVEN that you knew, may result in a law suit against you. That's why I recommend the precautionary measures in the demolition and why I recommend you as much of the 'piece-meal' work outside (not inside). You can contact your Waste Removal Service to see what you can do to throw it out. At worst, you'll have to take it to an incinerator. Sure, it will cost you a few $$$ but at least you know it's being properly disposed of. That's what the contractors do with it, and one of the reasons this type of jobs costs more than you'd expect.