Using the formula M1.V1 = M2.V2, your final concentration will be 6 mg/mL.
A concentration of 100 mg/mL or 100 mg/1000 uL indicates that each 10 uL of stock solution contains 1 mg analite. If we take 60 uL, that means we take 10 uL for 6 times. The analyte is 1 mg x 6 = 6 mg in 1000 uL; so, the final concentration is 6 mg/1000 uL or 6 mg/mL.