At present, laser cutting is currently employed to cut metallic plates, due to their good finish and dimensional quality, as well as because of the flexibility of the process to obtain different shapes. In the present paper, surface roughness, dimensional accuracy, and burr thickness of thin plates of 0.8 mm are studied as functions of different process parameters: pulse frequency, pulse width, and speed. Eight different experiments were performed according to a full 23 factorial design, with two replicates each. Square specimens of 10 mm × 10 mm were cut. Arithmetical mean roughness Ra was measured with a contact roughness meter, and the dimensions and burr thickness with a micrometer. Ra values ranged between 1.89 and 3.86 µm, dimensional error values between 0.22 and 0.93%, and burr thickness between 2 and 34 µm. Regression analysis was performed, and linear models were obtained for each response. Results showed that roughness depends mainly on frequency, on the interaction of frequency and pulse width and on pulse width. The dimensional error depends on pulse width, frequency, and the interaction between pulse width and speed. Burr thickness is influenced by frequency, pulse width, and the interaction between frequency and speed. Multi-objective optimization showed that, in order to simultaneously minimize the three responses, it is recommended to use high frequency (80 Hz), high pulse width (0.6 ms), and high speed (140 mm/min). The present study will help to select appropriate laser cutting conditions in thin plates, in order to favor good surface finish and dimensional accuracy, as well as low burr thickness.