Stack implementation using a singly linked list
This only works with int. Did you consider taking a template parameter so it can work with other types too?
Don't compare to nullptr. Instead use if (node) or if (!node).
You're very inconsistent with how you declare pointers. You have
Node* foo, Node * foo and Node *foo. Generally in C++ this is seen as part of the type so you should prefer the first variant.
You're using a member initialization list for Node but not for StackList. Why?
Prefer an early out when possible to avoid the build-up of arrow code.
Prefer prefix (++foo) over postfix (foo++) operator
Your comments add nothing to the code and can be removed.
Opinion based but you should not omit braces as it can lead to hard to find bugs.
The destructor can be implemented in terms of pop().
Node should be part of StackList as no one outside the class needs to access it. You could also simplify it by making it a struct and directly accessing the members.
You're violating the rule of three/five/zero by having a destructor/copy assignment operator but no move constructor or operator.
Your copy constructor does too much work. You can just iterate over the passed list and push(). Same for your assignment operator, look into the copy and swap idiom.