OK, as pointed out by several people above, the trick was not actually done by print(), it was done by the terminal itself to which print() was sending the string. I didn't realize that part, now it makes more sense. Thanks to all who pointed that out!

So, in the end, I will just treat it as a usual string manipulation case. Something like this:

i = mystr.rfind('\r')
newstr = mystr[i+1:]

It also works when the string doesn't contain '\r', because rfind() returns -1 in that case.