We use near-IR femtosecond laser pulses for a combination of microscopy and nanosurgery on fluorescently labeled structures within living cells. Three-dimensional reconstructions of microtubule structures tagged with green fluorescent protein (GFP) are made during different phases of the cell cycle. Further, the microtubules are dissected using the same laser beam but with a higher laser power than for microscopy. We establish the viability of this technique for the cells of a fission yeast, which is a common model to study the mechanics of cell division. We show that nanosurgery can be performed with submicrometer precision and without visible collateral damage to the cell. The energy is primarily absorbed by the GFP molecules, and not by other native structures in the cell. GFP is particularly suitable for multiphoton excitation, as its excitation wavelength near 900 nm is benign for most cellular structures. The ability to use GFP to label structures for destruction by multiphoton excitation may be a valuable tool in cell biology.