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We present a fast methodology to produce mock observations of the thermal and kinetic Sunyaev-Zel'dovich (SZ) effects based on the dark matter only $N$-body simulations coupled with the analytic intra-cluster medium model. The methods employ two different approaches: halo-based pasting (HP) and particle-based pasting (PP). The former pastes gas density and pressure onto halos and requires only a halo catalogue, and the latter considers the contribution from field particles as well, i.e., particles that do not belong to any halos and thus utilise the full particle information. Therefore, the PP algorithm incorporates secondary effects beyond the HP algorithm: asphericity of halos and contribution from diffuse gas. In particular, such a diffuse component is the dominant source of the kinetic SZ effect. As validation of our methods, we have produced 108 all-sky maps with HP and 108 flat-sky maps, which cover $5 \times 5 \, \mathrm{deg}^2$ with both HP and PP, and measured power spectra of the maps. Our method can produce a mock map within a few hours, even for all-sky coverage with a parallel computational environment. The power spectra of HP maps are consistent with the halo model prediction of the thermal SZ effect. On the other hand, the power spectra of PP maps are suppressed due to the halo asphericity but can reproduce better the theoretical prediction for the kinetic SZ effect. We discuss the utility of baryon-pasted mock SZ maps for estimating the covariance matrix of SZ statistics and modelling the selection and projection effects for cluster cosmology.