We report the observation of two-photon fluorescence excitation and cell confinement, simultaneously, in a continuous-wave (cw) single-beam gradient force optical trap, and demonstrate its use as an in-situ probe to study the physiological state of an optically confined cell sample. At the wavelength of 1064 nm, a single focused gaussian laser beam is used to simultaneously confine, and excite visible fluorescence from, a human sperm cell that has been tagged with propidium iodide, a exogenous fluorescent dye that functions as a viability assay of cellular physiological state. The intensity at the dye peak emission wavelength of 620 nm exhibits a near-square-law dependence on incident trapping beam photon laser power, a behavior consistent with a two-photon absorption process. In addition, for a sperm cell held stationary in the optical tweezers for a period of several minutes at a constant trapping power, red fluorescence emission was observed to increase the time, indicating that the cell has gradually transitioned between a live and dead state. Two-photon excited fluorescence was also observed in chinese hamster ovary cells that were confined by cw laser tweezers and stained with either propidium iodide or Snarf, a pH-sensitive dye probe. These results suggest that, for samples suitably tagged with fluorescent probes and vital stains, optical tweezers can be used to generate their own in-situ diagnostic optical probes of cellular viability or induced photodamage, via two-photon processes.