The structure and kinematics of the Milky Way disk are largely inferred from the solar vicinity. To gain a comprehensive understanding, it is essential to find reliable tracers in less-explored regions like the bulge and the far side of the disk. Mira variables, which are well-studied and bright standard candles, offer an excellent opportunity to trace intermediate and old populations in these complex regions. We aim to isolate a clean sample of Miras in the Vista Variables in the Via Lactea survey using Gaussian process algorithms. This sample will be used to study intermediate and old age populations in the Galactic bulge and far disk. Near- and mid-infrared time-series photometry were processed using Gaussian Process algorithms to identify Mira variables and model their light curves. We calibrated selection criteria with a visually inspected sample to create a high-purity sample of Miras, integrating multi-band photometry and kinematic data from proper motions. We present a catalog of 3602 Mira variables. By analyzing photometry, we classify them by O-rich or C-rich surface chemistry and derive selective-to-total extinction ratios of AKs/E(J-Ks)=0.471+/-0.01 and AKs/E(H-Ks)=1.320+/-0.020. Using the Mira period-age relation, we find evidence supporting the inside-out formation of the Milky Way disk. The distribution of proper motions and distances aligns with the Galactic rotation curve and disk kinematics. We extend the rotation curve up to RGC~17kpc and find no strong evidence of the nuclear stellar disk in our Mira sample. This study constitutes the largest catalog of variable stars on the far side of the Galactic disk to date.