To simplify the expression \((81x - 70y) - (63x + 34y)\), we'll first distribute the negative sign across the second set of parentheses:
\[ (81x - 70y) - (63x + 34y) = 81x - 70y - 63x - 34y \]
Next, we'll combine like terms. First, we'll combine the \(x\) terms:
\[ 81x - 63x = 18x \]
Now, we'll combine the \(y\) terms:
\[ -70y - 34y = -104y \]
Putting it all together, we have:
\[ 18x - 104y \]
Thus, the simplified expression is:
\[ \boxed{18x - 104y} \]
So the correct answer is D: \(18x - 104y\).