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Sound absorbing materials capable of working in harsh environments (e.g., fire resistance, moisture resistance, and pressure resistance) while having excellent low-frequency sound absorption properties are highly desirable for many practical applications. Recently, a new class of acoustic absorbers based on space coiling and folding metamaterials (SCFMs) has emerged. The SCFMs could be comprised of rigid plastics, ceramics, and metals and could be a good candidate for developing sound-absorbing devices capable of working in harsh environments. The SCFMs also enable flexible control of low-frequency sound with subwavelength structures, addressing the problem of poor absorption of low-frequency noise encountered by conventional acoustic materials. However, the current geometries of SCFM meta-atoms do not take full advantage of the configuration of three-dimensional space, limiting their ability for flexible control of sound absorption properties. Here, we propose an acoustic absorber based on stacked SCFMs with side openings, which could effectively absorb line-spectrum noise as well as broadband noise. The effects associated with the geometry and resonance modes of SCFMs are shown to significantly influence the sound absorption properties. To understand the sound-metamaterial interaction, an analytical model is obtained to study the acoustic response of SCFMs, which is further validated by numerical simulations. Further experiments have demonstrated the acoustic properties of our proposed metamaterial structure and confirmed the capability of stacked SCFMs for flexible control of the acoustic absorption spectrum. This work provides new possibilities for the development of novel sound absorption metamaterials desirable for many practical applications. [ABSTRACT FROM AUTHOR]