The optimum self-focussing materials with an intensity-dependent refractive index and the realization of the ability of these materials to produce intensity dependent phase shift in all-optical photonic devices have become a topic of continuous investigation. Many organic materials including dye-doped polymer films are creating interest due to their advantages in terms of enhanced efficiency, and optimum mechanical properties to fabricate reliable devices. In this paper, we have studied the nonlinear optical properties like nonlinear absorption and nonlinear refraction of a two-photon fluorescent dye DASPB doped in Polymethyl methacrylate-methacrylic acid (PMMA-MA) polymer matrix using open aperture and closed aperture Z-scan experimental methods by means of low power continuous wave (CW) laser beam. The optical limiting properties of these films are also studied using Type 1 and Type 2 configurations at different input powers using continuous wave (CW) laser beams of 532 nm wavelength. The nonlinear refractive index n2, nonlinear absorption coefficient β, changes in refractive index with input intensity, and the magnitude of third-order optical nonlinearity of the dye-doped film are experimentally determined. The saturated output power for type 1 and type 2 optical limiting are determined. The input limiting threshold and saturated output power level for both type 1 and type 2 optical limiting configurations are recorded. DASPB dye-doped in PMMA-MA polymer film has shown saturation absorption at lower input irradiance and reverse saturation absorption along with two-photon absorption at higher input irradiance and hence found to be a potential candidate for the third harmonic property based photonic devices.