As one of the main optical wireless communication technologies, visible light communication (VLC) is considered a promising supplement in 5G/6G and the internet of things (IoT) networks. The multiple-input–multiple-output (MIMO) multiplexing scheme can significantly enhance a VLC system’s performance. To handle the blind MIMO demultiplexing, geometric vector extraction (GVE) algorithms are used in a mixture space (MS), which has not been presented in the extant literature. In a 2 × 2 VLC MIMO scenario, the singular value decomposition of an arbitrary MIMO channel matrix is introduced to discuss the one-to-one relationship between channel-matrix elements and the outline-shape conversion starting from the transmitted rectangular-shaped points in the MS. By extracting the vector features of the adjacent sides of the received parallelogram-shaped constellation points, we can obtain the elements of an unknown channel matrix and recover the superposed signals transmitted by two light-emitting diodes (LED). To obtain a vector from these constellation points, clustering is required to obtain the scattered points’ centroids in advance. To avoid falling into a local minimum, we present a clustering algorithm with an initial-position-expansion pre-processing stage to place the initial centroids with the greatest accumulated distance. To enhance the computational efficiency, we enhance the clustering algorithm via a single iteration to obtain the centroids, which we named the GVE-for-iteration-once (GVE–IO) algorithm. The enhanced algorithm has an equivalent or better MIMO demultiplexing performance and quick convergence performance compared to the fast independent component analysis (FastICA) algorithm. Moreover, the GVE–IO algorithm’s computational complexity and measured running time is reduced to 29% and 23%, respectively, of the FastICA algorithm’ time costs. Finally, the experimental investigation shows that the proposed scheme exhibits a significantly reduced computational complexity in all discussed voltage peak-to-peak (Vpp) cases of LED and a Q-value enhancement in two-thirds of the Vpp combination regions for 50 input points.