This paper investigates multiuser interference (MUI) cancellation for millimeter-wave (mmWave) beamforming in extremely large-scale multiple-input multiple-output (XL-MIMO) communication systems. We propose a linear algorithm, termed iterative dual orthogonal projections (DOP), which alternates between two orthogonal projections: one to eliminate MUI and the other to refine combiners, ensuring a monotonic increase in spectral efficiency. Theoretical analysis and simulation results show that, with each iteration, the signal power for each user increases monotonically, the equivalent noise power after receive combining decreases monotonically, and the spectral efficiency improves accordingly and converges rapidly, closely approaching the theoretical optimum determined by dirty paper coding (DPC), outperforming existing linear algorithms in spectral efficiency.