Abstract: A method is for cutting a tubular structure in the petrochemical industry, using a cutting tool having a non-rotatable cutting element and a reaction member opposite to the non-rotatable cutting element. The cutting tool is further configured for carrying out a translational cutting movement through the tubular structure. The method comprises: a) positioning the cutting tool in a first position exterior to the tubular structure; b) squeezing the tubular structure at the first position by activating a partial translational cutting movement of the non-rotatable cutting element to obtain a dented region in the tubular structure; c) positioning the cutting tool in a second position exterior to the tubular structure, wherein the second position is displaced over a predefined distance compared to the first position, and d) cutting the tubular structure at the second position (P2) by activating a full translational cutting movement of the non-rotatable cutting element through the tubular structure.