Tapeworms can survive without many structures seen in other animals because of their thinness and close contact with the hosts from which they derive their nutrition. This allows them to directly absorb food and to expel waste across their surface, obviating the need for things like a mouth and an excretory system.
Work Step by Step
The key here is to realize that many animal systems are needed because of the size and complexity of the animals which have them. A flat animal in close contact with its food source, such as a tapeworm, can drop these structures and act more like a fungus, which is also simple and thin and in close contact with its food source.