Smart and connected communities (SCCs) are emerging as a novel paradigm that allows the community residents to be connected with surrounding environments through smart technologies. However, there remain important challenges to fully exploit the potential of SCCs in improving societal well-being and prosperity. In particular, there is a need for designing green communication systems that are also capable of providing high quality of service (QoS) to distribute and collect information to and from SCCs. However, simultaneously satisfying both of these criteria is difficult due to varying demands posed by heterogeneous sensing modalities, lack of dedicated infrastructure in rural/sub-urban areas, and certain sustainability constraints. While low-power short-range technologies often fail to achieve high QoS, using 3G or 4G technologies (LTE, LTE-A, GSM) for SCCs will eventually face spectrum scarcity and cross technology interference. In recent times, Dynamic spectrum access (DSA) has been proposed as a solution to overcome policy constraints and improve spectrum scarcity by spectrum sharing. In this article, we show that harnessing DSA in the context of SCCs can also achieve notable benefits in terms of energy efficiency and sustainability. Specifically, we propose a novel architecture for designing sustainable SCCs using a small-scale DSA-enabled overlay network that improves end-to-end energy efficiency of the network while guaranteeing QoS. We also propose a dynamic spectrum band selection approach that intelligently matches any message requirement to a suitable band type by exploiting distinct electro-magnetic characteristics of various bands. Since data generated in SCCs are typically valuable only when delivered within a certain hard (or soft ) deadline, we formulate a linear optimization problem for determining the most energy-efficient path that ensures a delivery time within the hard deadline. After proving that such a problem is NP-Hard, we propose an exact pseudo-polynomial time dynamic programming algorithm to solve it followed by a polynomial time greedy heuristic. Additionally, we formulate a non-linear optimization problem to find the optimal path when the message delivery time is defined as a soft deadline and extend our greedy heuristic to handle soft deadlines. Compared to the homogeneous band access approaches that opportunistically access free channels within a given spectrum band, our extensive simulation study shows that the proposed dynamic multi-band selection approach significantly improves the achievable energy efficiency while meeting various hard and soft deadlines.