The long propagation delay in underwater acoustic channels has attracted tremendous attentions in designing Medium Access Control (MAC). The low acoustic propagation speed and wide area of the acoustic communication range led to a wide range of variations in the propagation delay. This paper identifies an important characteristic of two-scale delay variations by field test results. We carry out simulations to study the impact of delay variations on MAC, and the results suggest a slot length adaptation scheme for the handshake and slotting based MAC. We further model an absorbing Markov chain to derive the closed-form equation for the throughput of MAC with adaptive slot length. Both the analytical and simulation results show that our proposed slot length adaptation improves significantly the throughput of MAC in underwater acoustic networks. Particularly, the Slotted-FAMA with an adaptive slot length achieves more than double the throughput than the Slotted-FAMA with a fixed slot length in a network with six nodes.