You don't give much information about how you made this soap, so it may be difficult to give good advice.
How did you use the activated charcoal? Did you mix it into a liquid first, such as water?
Did you give the white soap batter a good stir before you poured it into the mold? I bet you were working with the dark soap, while letting the white soap sit. Sometimes soap batter will get thicker as it sits, but it will loosen up a bit if you stir it gently with a spatula.
As far as the hardness at the bottom, it could be that the lye might have separated a little from the fats, and the soap at the bottom is a bit lye heavy. I am guessing this is not the case here, but it's a possibility.
Or you let the soap sit too long before cutting it. When it is best for cutting, soap should feel like a colby or mild cheddar cheese fresh from the refrigerator. It should not be hard like Parmesan cheese, and it should not be soft like cream cheese.
Or you used a knife to cut it rather than a wire or a flat blade. Knives have a triangular shape and as the knife blade gets close to the bottom, a brittle soap will often break apart rather than cut cleanly.
Or all of the above.