@onturenio, I think you should have a closer look at -Jproj|EPSG:n on the page provided by @seisman.
GMT is capable of using PROJ when linked against GDAL. You can now provide EPSG identifiers for your desired projection. You may ask what that’s good for. Well, the Web-Mercator projection, while not available in the traditional GMT syntax, has the EPSG identifier 3857.
So @seisman’s example will give you exactly what you are looking for. Try using -JEPSG:3857 and you should get your desired projection.