Autonomous mobile agents require low-power/energy-efficient machine learning (ML) algorithms to complete their ML-based tasks while adapting to diverse environments, as mobile agents are usually powered by batteries. These requirements can be fulfilled by Spiking Neural Networks (SNNs) as they offer low power/energy processing due to their sparse computations and efficient online learning with bio-inspired learning mechanisms for adapting to different environments. Recent works studied that the energy consumption of SNNs can be optimized by reducing the computation time of each neuron for processing a sequence of spikes (timestep). However, state-of-the-art techniques rely on intensive design searches to determine fixed timestep settings for only inference, thereby hindering the SNNs from achieving further energy efficiency gains in both training and inference. These techniques also restrict the SNNs from performing efficient online learning at run time. Toward this, we propose TopSpark, a novel methodology that leverages adaptive timestep reduction to enable energy-efficient SNN processing in both training and inference, while keeping its accuracy close to the accuracy of SNNs without timestep reduction. The ideas of TopSpark include: analyzing the impact of different timesteps on the accuracy; identifying neuron parameters that have a significant impact on accuracy in different timesteps; employing parameter enhancements that make SNNs effectively perform learning and inference using less spiking activity; and developing a strategy to trade-off accuracy, latency, and energy to meet the design requirements. The results show that, TopSpark saves the SNN latency by 3.9x as well as energy consumption by 3.5x (training) and 3.3x (inference) on average, across different network sizes, learning rules, and workloads, while maintaining the accuracy within 2% of SNNs without timestep reduction.