Single-cell nanosurgery and the ability to manipulate nanometer-sized subcellular structures with optical tweezers has widespread applications in biology but so far has been limited by difficulties in maintaining the functionality of the transported subcellular organelles. This difficulty arises because of the propensity of optical tweezers to photodamage the trapped object. To address this issue, this paper describes the use of a polarization-shaped optical vortex trap, which exerts less photodamage on the trapped particle than conventional optical tweezers, for carrying out single-cell nanosurgical procedures. This method is also anticipated to find broad use in the trapping of any nanoparticles that are adversely affected by high-intensity laser light.