The present study aimed to optimize the process parameters (milling depth and advanced speed) for an asphalt milling operation using a multi-response approach based on Taguchi design of experiments (DOE) and Grey Relational Analysis (GRA). Nine simulations tests were conducted using Discrete Element Method (DEM) in order to determine the forces acting on the cutting tooth support and tip. The considered performance characteristics were cutting forces (smaller is better category) and chip section area (larger is better category). A Grey Relational Grade (GRG) was determined from GRA, allowing to identify the optimal parameter levels for the asphalt milling process with multiple performance characteristics. It was found that that the optimal milling parameters for multi-response analysis are a milling depth of 200 mm and an advanced speed of 30 mm/min. Furthermore, analysis of variance (ANOVA) was used to determine the most significant factor influencing the performance characteristics. The analysis results revealed that the dominant factor affecting the resultant cutting force was milling depth, while the main factor affecting chip section area was the advanced speed. Optimizing milling efficiency is essential in machining operations. A key factor in this direction is comprehending the interplay between chip removal and cutting forces. This understanding is fundamental for achieving increased productivity, cost-effectiveness, and extended tool lifespan during the milling process.