From what I've seen, people generally recommend rope about 1/2" in width. 10mm is about 0.39 inches, so I would think based on width alone it would be ok.
There's other factors though. What is the material? Rope made of natural fiber is generally preferred to synethic. What is the strength rated to? Most rope should be tested to a "safe" weight capacity. If your rope is tested to a capacity of 175lbs, that might be enough if you weight 150lbs but it also could not be enough if you weigh 200lbs.