Metamaterial absorbers (MAs) serve as important electromagnetic wave-absorbing devices that have captured the attention of researchers for a long term. Functioning as sensitive detectors to determine perturbations in an ambient environment is another significant subsidiary function. Here, we theoretically propose an optimized fabrication method to implement terahertz MAs with fewer steps and also evaluate both absorption and sensing performances of such MAs realized by the new method. Simulation findings demonstrate that such MAs can basically maintain the original absorption features perfectly, including near-complete absorption at resonance as well as strong robustness to wide incident angles. Specifically, the full width at half-maximum and quality factor of the absorption resonances attenuate less than 26% and 8% with this new method, remaining in the ranges of $～0.03–0.04\mathrm{THz}$ and $～20–27$ for two selected example MAs. More significantly, sensing capacities of this type of MA, in terms of maximum detection range (enhancing at least 9%), observable spectral modulation (increasing at least 6.3%), and refractive index sensitivity, are improved to a large extent because of more intense coupling between resonant field and matter in the case of surface-relief MAs. This stronger coupling results from exposing more spots of the resonantly high field to direct contact with an approaching analyte, which is illustrated by field profiles of the MAs at resonance in this work. Additionally, other desirable absorber features are also explored with such MAs, like functioning as building blocks to configure multiband MAs and strong robustness against fabrication errors. Such new-style terahertz MAs shown in the paper, acting as good examples, not only prove that terahertz MAs can be fabricated by the proposed time- and cost-saving route in contrast to the traditional MA fabrication process, but also can serve as novel platforms to explore other intriguing terahertz photonic effects, such as the field enhancement effect.