We conducted an optical monitoring survey of the Sagittarius dwarf irregular galaxy (SagDIG) during the period of 2016 June-2017 October, using the 2.5 m Isaac Newton Telescopeat La Palama. Our goal was to identify long-period variable stars (LPVs), namely, asymptotic giant branch stars (AGBs) and red supergiant stars, to obtain the star formation history of isolated, metal-poor SagDIG. For our purpose, we used a method that relies on evaluating the relation between luminosity and the birth mass of these most evolved stars. We found 27 LPV candidates within 2 half-light radii of SagDIG. 10 LPV candidates were in common with previous studies, including one extreme-AGB (x-AGB). By adopting the metallicity Z = 0.0002 for older populations and Z = 0.0004 for younger ages, we estimated that the star formation rate changes from 0.0005 ± 0.0002 M ⊙ yr-1 kpc-2 (13 Gyr ago) to 0.0021 ± 0.0010 M ⊙ yr-1 kpc-2 (0.06 Gyr ago). Like many dwarf irregular galaxies, SagDIG has had continuous star formation activity across its lifetime, though with different rates, and experiences an enhancement of star formation since z ≃ 1. We also evaluated the total stellar mass within 2 half-light radii of SagDIG for three choices of metallicities. For metallicity Z = 0.0002 and 0.0004, we estimated the stellar mass M* = (5.4 ± 2.3) × 106 and (3.0 ± 1.3) × 106 M ⊙, respectively. Additionally, we determined a distance modulus of μ = 25.27 ± 0.05 mag, using the tip of the red giant branch.