Single point diamond machining (SPDM) produces smooth machined surfaces that other production methods cannot match. While the mechanics of machining of cast alloys with SPDM is well-explored, the realm of SPDM for additively manufactured parts remains largely uncharted. This work reveals new insights into the surface generation process of an additively manufactured titanium alloy, specifically, a Ti6Al4V Extra Low Interstitials (ELI) alloy workpiece. Our examination of the chip morphology unveiled a distinct mode of chip removal, previously unrecorded in existing literature. During SPDM of additively made Ti6Al4V ELI workpiece, identification of numerous pores and discontinuities in the chips flowing on the tool rake face, indicating periodic intermittent cracking during the material's plastic flow was seen. To examine this phenomenon, a finite element analysis (FEA) model was developed. While the FEA model can well explain the machining mechanics and chip morphology of SPDM of cast Ti6Al4V ELI reported in the literature, it failed to describe the chip morphology that are obtained during machining of additively made workpiece in this work. This disparity underscores the need for innovative simulation approaches tailored for additively manufactured components. The experimental observations in this study highlight a unique form of chip formation in contrast to conventional Ti6Al4V alloy machining processes. At lower feeds, there was a presence of short, discontinuous chip formation with tearing at the outer periphery. Conversely, at higher feeds, a long, continuous ribbon-like chip formation was observed. In addition, some typical additive manufacturing defects appear on the machined surface and chips. Through optimisation of the SPDT parameters, a surface roughness (Ra) value of about 11.8 nm was achieved on additively manufactured Ti6Al4V ELI workpiece. This work provides a fresh perspective on the mechanics of SPDM for additively manufactured components, offering a stepping stone for subsequent studies.