Mobile crowdsensing (MCS) is a promising paradigm where sensor-embedded mobile devices are exploited for collecting and sharing environmental data. In MCS, the participating mobile devices collect the required data, (pre-)process the data and transmit the data and/or pre-processing results to the server for further processing. In wireless edge networks, transmission and/or processing of sensed data may be unsuccessful due to unstable wireless channels, limited bandwidth, energy and computation resources. To optimize MCS performance, it is imperative to jointly design the data sensing, processing and transmission policies under resource constraints. In this paper, we propose a joint sensing, communication and computation (JSCC) framework for multi-dimensional resource constrained MCS systems. We formulate the JSCC design as an optimization problem, by jointly controlling the data sensing, transmission and computation offloading processes in the system. Simulation results show that the proposed JSCC framework significantly outperforms several baseline solutions without jointly considering data sensing-transmission-computation and/or multi-dimensional resource limitations.