You mention "oceans", certainly we have huge aquifers in the world (Ogallala in the US is a big one; 174,000 square miles, bigger than the Caspian Sea (at 143,000 sq mi). Here are other aquifers).
A world heavily dotted with a network of such aquifers could have no oceans; but I imagine there would still be a water cycle above ground: Plants could access the water, but evaporate it by normal biology; there would still be some cloud cover and rains due to concentrations caused by planet rotation winds: Just the rain doesn't accumulate, it percolates back down into the aquifers.
I don't think you can have surface plants without them producing water vapor, by drying out (especially upon death) or burning: water is not destroyed by burning, it just becomes steam and escapes (and must go somewhere). If water vapor is produced, an above ground water cycle would exist.
If the plants only grow under ground, the evaporation can be absorbed by the earth or rock ceiling. If they grow under water there is no evaporation, but there could be a cycle of exchange between plant fluids and the water.
added: Animals on such a planet would evolve to get their water from the food they eat; ultimately traceable back to the water the plants are bringing up from the aquifers. IRL we do have animals that only get water from their food, I can't recall which ones off-hand, but it isn't a stretch for evolution. In any case, having gotten their water, they would still eliminate it, by sweat, saliva / panting, tears, urination and defecation. Those in turn would evaporate and dry, contributing vapor to the water cycle, which would collect and become rain. Some animals would evolve (like we have in the deserts, IRL) to get all their water during the rains, and store it within their bodies to be used slowly, in-between the rains.