Depending on the geometry of your particular installation, do think of
using a hydraulic jack to lift one corner of your slab, then run
timbers or pipes underneath, and move the jack to the next contact
point. You will probably have to dig a fair amount under the slab to
slip in your jack, and put a stout piece of 2 by 6 under it as a
platform. Most car hydraulic jacks will lift 2 tons easily. The
bottle shaped jacks have a small footprint, but they must be set in 8
inches or so under the slab, lower-profile versions may need as little
as 4 inches of headroom under the slab. The hardest part of this is
digging the access hole.
I used this technique to demolish a misaligned slab which was
funneling water into an angle of a basement wall. One 36 inch long
side fronted on a gravel drive, so it was easy to dig up and put the
jack underneath. I put a few 6 x 6 timbers under each end, then after
a few mighty hammer blows, the slab was in manageable pieces.
Originally I was intending to move the slab into a better position,
but found it was easier to demolish the old slab and pour a new one in
proper alignment.