With the development of edge networks and mobile computing, the need to serve heterogeneous data sources at the network edge requires the design of new distributed machine learning mechanisms. As a prevalent approach, Federated Learning (FL) employs parameter-sharing and gradient-averaging between clients and a server. Despite its many favorable qualities, such as convergence and data-privacy guarantees, it is well-known that classic FL fails to address the challenge of data heterogeneity and computation heterogeneity across clients. Most existing works that aim to accommodate such sources of heterogeneity stay within the FL operation paradigm, with modifications to overcome the negative effect of heterogeneous data. In this work, as an alternative paradigm, we propose a Multi-Task Split Learning (MTSL) framework, which combines the advantages of Split Learning (SL) with the flexibility of distributed network architectures. In contrast to the FL counterpart, in this paradigm, heterogeneity is not an obstacle to overcome, but a useful property to take advantage of. As such, this work aims to introduce a new architecture and methodology to perform multi-task learning for heterogeneous data sources efficiently, with the hope of encouraging the community to further explore the potential advantages we reveal. To support this promise, we first show through theoretical analysis that MTSL can achieve fast convergence by tuning the learning rate of the server and clients. Then, we compare the performance of MTSL with existing multi-task FL methods numerically on several image classification datasets to show that MTSL has advantages over FL in training speed, communication cost, and robustness to heterogeneous data.