Thank you very much for even bothering to actually edit it! I succeeded!
By your instruction, I found out that the critical step is to "detach" the part I selected by faces as a new object!
Sorry for wrongly refering to the "parts/elements" as "groups". I referred so because that's the term used in obj file format. It seems that the naming in 3ds max is different.
To help others with the same proplem,
here is how I cut a forearm apart and export it as a new obj file :
Select the element ( or object, or in terms of obj format : group ) containing the forearm you want,
then right-click the mouse on the element/object, and choose "convert to editable mesh".
Now the right panel will show several selection units for you to choose,
choose the unit as "face" by clicking a triangle icon there.
Drag-select the forearm to make it red, then right-click on it , select "detach".
A window pops out asking you to name the new object, which is the forearm.
After this, the forearm would be isolated from the old element/object and become a new object itself.
Select the forearm object, and click the most top-left button on the 3ds max window,
select "export" -> "export selected", and choose the file type as obj. Done.
Sorry for writting in such details,
because I assume that people who have the same problem as me would be as unfamiliar with 3ds max as me, HaHa.
Thank you again!