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Creating and maintaining the Metaverse requires enormous resources that have never been seen before, especially computing resources for intensive data processing to support the Extended Reality, enormous storage resources, and massive networking resources for maintaining ultra high-speed and low-latency connections. Therefore, this work aims to propose a novel framework, namely MetaSlicing, that can provide a highly effective and comprehensive solution in managing and allocating different types of resources for Metaverse applications. In particular, by observing that Metaverse applications may have common functions, we first propose grouping applications into clusters, called MetaInstances. In a MetaInstance, common functions can be shared among applications. As such, the same resources can be used by multiple applications simultaneously, thereby enhancing resource utilization dramatically.To address the real-time characteristic and resource demand's dynamic and uncertainty in the Metaverse, we develop an effective framework based on the semi-Markov decision process and propose an intelligent admission control algorithm that can maximize resource utilization and enhance the Quality-of-Service for end-users. Extensive simulation results show that our proposed solution outperforms the Greedy-based policies by up to 80% and 47% in terms of long-term revenue for Metaverse providers and request acceptance probability, respectively.