Hi,
There is no option to do that. The cart is common to all the products.
It's possible to have several carts but there is not a ready made mechanism where you can tell the system to switch the cart based on the category.
With a custom plugin developed for that it should be possible though.
But maybe there is another solution to what you're trying to do ? Could you explain why you need to do that ? What should happen after a product has added products to a cart ? Won't he purchase the products in it ? In that case, instead of adding the second set of products in a new cart, why not block the user from adding products from another category in the cart ? Might that be a possibility ?