Network applications and users have very diverse service expectations and requirements, demanding for provisioning different levels of quality of service on the Internet. As the speed of network links has been rising at a pace that exceeds that of the growth in the buffer size, packet loss rate differentiation has been an active research topic. However, none of the existing packet dropping schemes for loss rate differentiation considered an important issue, that is, the retransmission overhead of dropped packets. In this paper, we design a hop-count based probabilistic packet dropper (HPPD) for congestion mitigation and loss rate differentiation. HPPD aims to meet a unique two-fold objective by two-dimensional loss rate differentiation: the primary one is the congestion mitigation that aims to reduce congestion in the first place by dropping intra-class packets differently based on their maturity levels to reduce retransmission cost; the other is inter-class proportional loss rate differentiation. The maturity level of a packet, the number of hops it has travelled, is inferred from its time-to-live value in the IP header. We propose a novel intra-class nth-root proportional dropping scheme. The scheme reduces retransmission cost by giving higher dropping probabilities to less mature packets while all packets have their forwarding chances. The n is a controllable parameter trading off dropping fairness for congestion mitigation. It provides great controllability to network operators. Simulation results show that HPPD can significantly mitigate the congestion by reducing the retransmission overhead of dropped packets and achieve the proportional loss rate differentiation at the same time.