Capri is an island quite a few miles off the coast of Italy (Sorrento is about the closest and is still a 20 min fast boat ride from the island) so you cannot take a taxi from Naples to Capri unless that taxi can either fly through the air or plow through the sea
. The two most popular ways of getting to Capri are via jetboat/hydrofoils from either Naples or Sorrento. There is also less frequent service between Capri and Positano, Amalfi and Salerno.
If you did mean "water taxi" we are not aware of any water taxi service from Naples to Capri as it would take a slower boat about 1 1/2 hours each way and cost a fortune.