Asphalt is a ton easier to remove than concrete. I would remove it myself. Try getting under one edge and prying up with a wrecking bar or just pull up with a pickaxe. Experiment and you will find that it comes apart with some effort. You can use the scraps for filling in somewhere else on your lot, bury it, or get someone to take it away. If it is tough just prying it then you could rent a concrete cutting saw, which is just a big skill saw with an abrasive masonry blade. You then just cut straight lines in a checkerboard so that each piece will break away easier. Or, you could do the same thing with an electric jackhammer that you rent at a tool rental shop, same checkerboard. This shouldn't be too too tough. Probably easier in the summer when it is a little softer, but then it is hot for you to do heavy work too.