Training large neural networks with meaningful/usable differential privacy security guarantees is a demanding challenge. In this paper, we tackle this problem by revisiting the two key operations in Differentially Private Stochastic Gradient Descent (DP-SGD): 1) iterative perturbation and 2) gradient clipping. We propose a generic optimization framework, called {\em ModelMix}, which performs random aggregation of intermediate model states. It strengthens the composite privacy analysis utilizing the entropy of the training trajectory and improves the $(ε, δ)$ DP security parameters by an order of magnitude. We provide rigorous analyses for both the utility guarantees and privacy amplification of ModelMix. In particular, we present a formal study on the effect of gradient clipping in DP-SGD, which provides theoretical instruction on how hyper-parameters should be selected. We also introduce a refined gradient clipping method, which can further sharpen the privacy loss in private learning when combined with ModelMix. Thorough experiments with significant privacy/utility improvement are presented to support our theory. We train a Resnet-20 network on CIFAR10 with $70.4\%$ accuracy via ModelMix given $(ε=8, δ=10^{-5})$ DP-budget, compared to the same performance but with $(ε=145.8,δ=10^{-5})$ using regular DP-SGD; assisted with additional public low-dimensional gradient embedding, one can further improve the accuracy to $79.1\%$ with $(ε=6.1, δ=10^{-5})$ DP-budget, compared to the same performance but with $(ε=111.2, δ=10^{-5})$ without ModelMix.