In the field of histopathology, the microtomy procedure yields thin sections of tissue embedded in paraffin blocks, then to be further processed for diagnostic purposes. Within microtomy, trimming is an initial but critical process in which the excess paraffin covering the tissue of interest is removed by continuous cutting routines, until the tissue is suitably exposed and ready for sectioning. Trimming is currently a time-consuming process that is manually held by technicians. In this paper, we present a method to automatize this process, by analyzing tissue block surface images resulting from each cyclic cutting routine. Two types of Convolutional Neural Networks (CNNs) were fine-tuned: one for binary segmentation, the other for multi-class classification tasks, by exploring and optimizing lightweight architectures to provide fast analytical results on cost-effective edge computing. Two sequential online conditions followed the CNNs to output the current stage of the block surface and rule if the trimming-end cutting routine was reached. We compared the results obtained through our method with the ones obtained by three skilled technicians processing 75 tissue blocks. The proposed method identified the trimming-end cutting routine approximately as accurate as the technicians did, yielding up to 90% of trimmed blocks of optimal quality and evidencing the potential of this tool in future automated trimming instruments. We deployed our method to an Edge TPU hardware accelerator to showcase its capability to provide immediate and objective results at every microtomy station applied with an ad hoc hardware, potentially guaranteeing a throughput 50% higher than manual trimming.