How do I carve a rat/cat?!?!?!?

Why is is impossible? Is it still in powder form? If so it probably needs to be mixed with the correct amount of water and your teacher must have given you instructions for it. Are you sure it's not plaster? You can carve plaster with a kitchen knife or even with a spoon.

First you have to get a reasonably clear idea how your animal fits into the block of whatever. Maybe it will help you if you make some drawings. Draw an outline around your paper cup and try how your animal will fit into it. Also try to make it as compact as possible - have the tail would around the animal, don't try to carve it free, have feet and legs close to the body (e.g. a sleeping cat can have its paws tightly tucked under its body.). You can use a pencil to draw outlines of your animal on the block to help you to get the proportions right before you get going. Look at pictures of caroon animals, they are already simplified, so you they will be easier to carve than trying to get it as naturalistic as possible.

If you are having trouble seeing it in the subtractive process

You can make a piece by the additive process and then start carving the block. In other words you can make a rat in clay that would fit in the block. Then you can refer to your clay rat while carving the block.

I have known wood carvers that would make something in oil based clay before they would carve something more difficult in wood.

The best way to learn to carve is to watch someone else carve then try doing it yourself. Try to think 2 steps ahead. Sometimes a chip is removed in 2 steps. A stop cut is made then a second cut is made to the stop cut to remove the chip.

If the thing is next to impossible because it is too hard, you might ask your teacher for a softer material

http://www.ask.com/web?q=+artistic+carving+animals...

Same way as you would carve a dog or cow.