Laser Beam machining (LBM) nowadays finds a wide acceptance for cutting various materials and cutting of polymer sheets is no exception. Greater reliability of process coupled with superior quality of finished product makes LBM widely used for cutting polymeric materials. Earlier researchers investigated the carbon dioxide laser cutting to a few thermoplastic polymers in thickness varying from 2mm to 10mm. Here, an approach is being made for grading the suitability of polymeric materials and to answer the problem of selection for LBM cutting as per their weightages obtained by using multi-decision making (MCDM) approach. An attempt has also been made to validate the result thus obtained with the experimental results obtained by previous researchers. The analysis encompasses the use of non-parametric linear-programming method of data envelopment analysis (DEA) for process efficiency assessment combined with technique for order preference by similarity to an ideal solution (TOPSIS) for selection of polymer sheets, which is based on the closeness values. The results of this uniquely blended analysis reflect that for 3mm thick polymer sheet is polypropelene (PP) to be highly preferable over polyethylene (PE) and polycarbonate (PC). While it turns out to be that polycarbonate (PC) to be highly preferable to other two polymers for 5mm thick polymer sheets. Hence the present research analysis fits very good for the polymer sheets of 3mm thickness while it deviates a little bit for the 5mm sheets.