I don't lift logs to cut them up. I use a wedge to just spread the cut and lift the logs simultaneously.
I haven't been able to find a video demonstrating this technique, so you'll just have to trust me. It works. I have lifted 4' diameter logs off the ground several inches with nothing more than a chainsaw, wedge, and sledge. And it is faster and easier than you would ever imagine until you have tried it.
Say you've got a big log that fell onto soft ground and sunk into a depression. For whatever reason, you don't want to cut down to the ground, you'd like to lift that log, and it is far too big and heavy to consider rolling over to finish the cut.
Start your cut deep enough to set the wedge safely, then finish the cut to down to where you need ground clearance. Pound in the wedge, which will separate the two log sections along the cut you have installed. This has so much force, that the ends o the log will be pressing down, and the middle of the log (where your cut is) will be lifted clear of the ground.
The only time this doesn't work is when your log is too narrow diameter to get the wedge in, or when your cut is so near one end of the log that you don't get enough lift to clear the ground obstructions. I guess if the ground is just to soft, it will not work, either.
I suppose if you are working on a big enough tree, it might not work, but they don't come that big around here. The bigger the tree, the more likely I am to make sure I don't forget to bring the wedges.
NOTE: practice your cutting techniques a bit more. It isn't essential to lift a log to cut them through all the way. You don't really think those lumberjacks cutting up the 200' tall douglas fir trees are lifting those logs with a farm-jack to buck them up, do you?