As a revolutionary paradigm for intelligently controlling wireless channels, intelligent reflecting surface (IRS) has emerged as a promising technology for future sixth-generation (6G) wireless communications. While IRS-aided communication systems can achieve attractive high channel gains, existing schemes require plenty of IRS elements to mitigate the ``multiplicative fading'' effect in cascaded channels, leading to high complexity for real-time beamforming and high signaling overhead for channel estimation. In this paper, the concept of sustainable intelligent element-grouping IRS (IEG-IRS) is proposed to overcome those fundamental bottlenecks. Specifically, based on the statistical channel state information (S-CSI), the proposed grouping strategy intelligently pre-divide the IEG-IRS elements into multiple groups based on the beam-domain grouping method, with each group sharing the common reflection coefficient and being optimized in real time using the instantaneous channel state information (I-CSI). Then, we further analyze the asymptotic performance of the IEG-IRS to reveal the substantial capacity gain in an extremely large-scale IRS (XL-IRS) aided single-user single-input single-output (SU-SISO) system. In particular, when a line-of-sight (LoS) component exists, it demonstrates that the combined cascaded link can be considered as a ``deterministic virtual LoS'' channel, resulting in a sustainable squared array gain achieved by the IEG-IRS. Finally, we formulate a weighted-sum-rate (WSR) maximization problem for an IEG-IRS-aided multiuser multiple-input single-output (MU-MISO) system and a two-stage algorithm for optimizing the beam-domain grouping strategy and the multi-user active-passive beamforming is proposed.