First of all I must say that I didn't understand much of the problem, nor did I ever work with tiles or the SetSubRect function.
But I notice one thing: if I look at the code I think that you want to draw squares.
This are the values that u pass to the rectangle:
sf::IntRect Rect(0, 60, 60, 120);
The last number is not the bottom position, but the height. If you were drawing squares then this should be 60.
Also if you wanted the top left piece of your image then the second number should be 0.
But if this is not the problem, then could you please try to explain the problem a little bit better?