Turning with rotary tool is a newly developed alternative of the conventional turning process in which cutting edge of a round insert rotates about its axis, so that a continuously indexed cutting edge is fed into the cutting zone. In the present study, a longitudinal high-frequency vibration was superimposed to the rotary tool to analyze the cutting force and surface roughness of AA7075 during orthogonal cutting. However, due to contribution of wide ranges of factors in the vibratory-rotary turning process, the selection of optimal parameter setting is a challenge that is faced with this process. In the present work, an attempt was made to simultaneously minimize machining force ( Fz) and surface roughness ( Ra) through selection of the optimal setting of cutting velocity, feed rate, tool rotary speed in rotary turning, and vibratory-rotary turning operations. Here, grey relational analysis was used to find the optimal parameter setting in rotary turning and vibratory-rotary turning processes, separately. Then the obtained solutions were compared. Results indicated that applying axial vibration to the rotary tool turning significantly reduced both surface roughness and cutting force. From the optimization by the grey relational analysis method, it was obtained that for both rotary turning and vibratory-rotary turning operations, setting of 4 m/min cutting velocity, 220 r/min tool rotary speed, 0.08 mm/rev feed rate, and 0.3 mm depth of cut are the most-optimal solutions that causes minimum Fz and Ra, simultaneously. Also, the vibratory-rotary turning process had higher values of grey relational grade than the rotary turning process that implies outperformance of the vibratory-rotary turning with respect to the rotary turning process. The obtained results were then verified, compared, and discussed based on the mechanics of turning process.