We provide experimental evidence that the laser beam scanning strategy has a significant influence on material removal rate in the ultrafast laser machining of glass. A comparative study of two laser beam scanning methods, (i) bidirectional sequential scanning method (SM) and (ii) bidirectional interlaced scanning method (IM), is presented for micromachining 1.1-mm-thick borosilicate glass plates (Borofloat® 33). Material removal rate and surface roughness are measured for a range of pulse energies, overlaps, and repetition frequencies. With a pulse overlap of ≤90%, IM can provide double the ablation depth and double the removal rate in comparison to SM, whilst maintaining very similar surface roughness. In both cases, the root-mean-square (RMS) surface roughness (Sq) was in the range of 1 μm to 2.5 μm. For a 95% pulse overlap, the difference was more pronounced, with IM providing up to four times the ablation depth of SM; however, this is at the cost of a significant increase in surface roughness (Sq values >5 μm). The increased ablation depths and removal rates with IM are attributed to a layer-by-layer material removal process, providing more efficient ejection of glass particles and, hence, reduced shielding of the machined area. IM also has smaller local angles of incidence of the laser beam that potentially can lead to a better coupling efficiency of the laser beam with the material.