We present TropNNC, a framework for compressing neural networks with linear and convolutional layers and ReLU-type activations using tropical geometry. By representing a network's output as a tropical rational function, TropNNC enables structured compression via reduction of the corresponding tropical polynomials. Our method identifies redundancy via similarity and improves upon the geometric approximation of previous work by adaptively selecting the weights of retained neurons. We relate it to SVD and spectral clustering, and provide insights into network compression beyond the specific setting considered. We provide the tightest known theoretical compression bound, and the first successful application of tropical geometry to convolutional layers. TropNNC requires access only to network weights - no training data - and achieves competitive performance on MNIST, CIFAR, and ImageNet, matching strong baselines such as ThiNet and CUP.

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