A family of low-complexity detection schemes based on channel matrix puncturing targeted for large multiple-input multiple-output (MIMO) systems is proposed. It is well-known that the computational cost of MIMO detection based on QR decomposition is directly proportional to the number of non-zero entries involved in back-substitution and slicing operations in the triangularized channel matrix, which can be too high for low-latency applications involving large MIMO dimensions. By systematically puncturing the channel to have a specific structure, it is demonstrated that the detection process can be accelerated by employing standard schemes such as chase detection, list detection, nulling-and-cancellation detection, and sub-space detection on the transformed matrix. The performance of these schemes is characterized and analyzed mathematically, and bounds on the achievable diversity gain and probability of bit error are derived. Surprisingly, it is shown that puncturing does not negatively impact the receive diversity gain in hard-output detectors. The analysis is extended to soft-output detection when computing per-layer bit log-likelihood ratios; it is shown that significant performance gains are attainable by ordering the layer of interest to be at the root when puncturing the channel. Simulations of coded and uncoded scenarios certify that the proposed schemes scale up efficiently both in the number of antennas and constellation size, as well as in the presence of correlated channels. In particular, soft-output per-layer sub-space detection is shown to achieve a 2.5dB SNR gain at $10^{-4}$ bit error rate in $256$-QAM $16\!\times\!16$ MIMO, while saving $77\%$ of nulling-and-cancellation computations.