As Additive Manufacturing (AM) continues gaining momentum with greater applications, several sustainability assessment methods for AM have emerged in recent times. However, these methods are typically limited in scope and applicability. A review of existing literature on AM process sustainability metrics reveals that a wide variety of the previously proposed AM sustainability evaluation methods consider only environmental and economic aspects, as opposed to the Tripple-Bottom-Line (Environmental, Societal, and Economic). This paper presents a more comprehensive metrics-based methodology for evaluating the sustainability of AM processes to address the shortcomings of the previously established sustainability evaluation methods. To demonstrate the application of the developed method, a numerical case study on Laser Powder Bed Fusion (LPBF) was conducted to evaluate the sustainability of the process, considering the pre-manufacturing and manufacturing stages of the product life cycle. The results enable evaluating the key benefits and tradeoffs with LPBF demonstrating that the metrics-based method proposed in this paper can effectively evaluate the AM process's sustainability performance.