Summatory function of Moebius and Euler's totient function over $y$-smooth numbers

Question

Let $y \geq 1$. We say that a positive integer $n$ is $y$-smooth if $n$ has no prime factors larger than $y$. Let $x \geq y$. Let $\mu$ and $\varphi$ be the Moebius and Euler's totient function respectively. What are good upper bounds for the absolute value of the sum $$ S(x,y) = \sum_{\substack{n \leq x \\ n \text{ is } y-\text{smooth}}}\mu(n)? $$ For the following sum, can we give a good lower bound? $$ T(x,y) = \sum_{\substack{n \leq x \\ n \text{ is } y-\text{smooth}}}\varphi(n) $$