Impact of removing all organisms of a trophic level is different for different trophic levels.
For example, if we remove producers from a food chain, no organism will get food, if we remove herbivores from a food chain then carnivores will die and producers will also die due to competition for space and nutrients. No, we can't remove any trophic level without causing damage to the ecosystem as one is dependent on other for their survival. If we remove any one this will create imbalnce in the ecosystem.