The growing diversification of mobile services imposes requirements on network performance that are ever more stringent and heterogeneous. Network slicing aligns mobile network operation to this context, by enabling operators to isolate and customize network resources on a per-service basis. A key input for provisioning resources to slices is real-time information about the traffic demands generated by individual services. Acquiring such knowledge is however challenging, as legacy approaches based on in-depth inspection of traffic streams have high computational costs, which inflate with the widening adoption of encryption over data and control traffic. In this paper, we present a new approach to service-level demand estimation for slicing, which hinges on decomposition, i.e., the inference of per-service demands from traffic aggregates. By operating on total traffic volumes only, our approach overcomes the complexity and limitations of legacy traffic classification techniques , and provides a suitable input to recent 'Network Slice as a Service' (NSaaS) models. We implement decomposition through Microscope, a novel framework that uses deep learning to infer individual service demands from complex spatiotemporal features hidden in traffic aggregates. Microscope (i) transforms traffic data collected in irregular radio access deployments in a format suitable for convolutional learning, and (ii) can accommodate a variety of neural network architectures, including original 3D Deformable Convolutional Neural Networks (3D-DefCNNs) that we explicitly design for decomposition. Experiments with measurement data collected in an operational network demonstrate that Microscope accurately estimates per-service traffic demands with relative errors below 1.2%. Further, tests in practical NSaaS management use cases show that resource allocations informed by decomposition yield affordable costs for the mobile network operator.