Assuming you are in a pressurised plane, you wouldn't be able to stick your head out, as you would be sucked out through the hole due to explosive decompression!
If you did survive the decompression and by some miracle half the planes fuselage wasnt missing by this point, and it could still fly, your head would freeze, also the air is too thin to breathe, and the lack of pressure would cause the liquids and gasses in your head to expand, thus popping it like a baloon, in other words leave the hacksaw in the luggage compartment!
I'd just like to add to what dinsdale says. You would be putting your head out into a 480-odd m.p.h. wind, so while the expansion of liquids in your head would force your eyes out of their sockets, the wind would drive them back in. It would force your lips very wide open and blow your mouth up like a football, dislocating your jaw. It would inflate and tear your nostrils. You wouldn't be a pretty sight.
However, this would not worry you. The wind would have bent your head back and broken your neck almost before all these other interesting things happened (but not quite). Please have someone video the moment for the entertainment of the rest of us.
I am fascinated how you got the means to cut "the hole in the plane" on board in the first place - I can only assume you must be a journalist for one of the tabloids.
These mythys about small holes in pressurised aircraft fuselages causing the plane to de-pressurise in seconds or worse, tear it's self apart and crash, are just that - myths! Aircraft fuselages leak like seives anyway and the compressors have enough over capacity to compensate for even large holes - a modern airliner will still hold cabin pressure with several windows missing. Planes do loose bits of fuselage or doors from time to time - there was one that lost a third of it's cabin roof and still landed safely.
J