The distribution of ejecta in young supernova remnants offers a powerful observational probe of their explosions and progenitors. Here we present a 3D reconstruction of the ejecta in SNR 0540-69.3, which is an O-rich remnant with a pulsar wind nebula located in the LMC. We use observations from VLT/MUSE to study Hbeta, [O III] lambda lambda 4959, 5007, Halpha, [S II] lambda lambda 6717, 6731, [Ar III] lambda 7136 and [S III] lambda 9069 emission lines. This is complemented by 2D spectra from VLT/X-shooter, which also cover [O II] lambda lambda 3726, 3729 and [Fe II] lambda 12567. We identify three main emission components: (i) Clumpy rings in the inner nebula (<1000 km/s) with similar morphologies in all lines; (ii) Faint extended [O III] emission dominated by an irregular ring-like structure with radius ~1600 km/s and inclination ~40 dg, but with maximal velocities reaching ~3000 km/s; and (iii) A blob of Halpha and Hbeta located southeast of the pulsar at velocities ~1500-3500 km/s. We analyze the geometry using a clump-finding algorithm and use the clumps in the [O III] ring to estimate an age of 1146 pm 116 years. The observations favor an interpretation of the [O III] ring as ejecta, while the origin of the H-blob is more uncertain. An alternative explanation is that it is the blown-off envelope of a binary companion. From the detection of Balmer lines in the innermost ejecta we confirm that SNR 0540 was a Type II supernova and that hydrogen was mixed down to low velocities in the explosion.
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