I need to Improve drainage in croncrete
Yes, you can cut concrete.  You could hire someone with a concrete saw to do the work, or you can buy a masonry blade for a standard circular saw.  Make sure you wear goggles and a mask to keep concrete dust and chips out of your eyes and lungs.   It is noisy (and slow) so please wear ear plugs also.

You will have to make sure the trench slopes towards the drain, of course.

If you have a blade that works in dry or wet, there will be less dust if you can cut it wet or dampened.  You can use a standard electric circular saw if the concrete is dampened, but make sure it is grounded properly for safety.  If you need to cut through standing water, use a gas powered saw (you can rent these).

This is an example of a good masonry blade, available from many sources.