The Windows Runtime string type, HSTRING is immutable and is reference counted.
The Platform::String type in C++/CX is simply a wrapper around the HSTRING type and the handful of operations that it supports (see the functions that start with Windows in the Windows Runtime C++ Functions list).
There are no operations that mutate the string because the string type is immutable (hence why there is no Replace). There are a few non-mutating operations (certainly fewer than C++'s std::wstring).
Platform::String does provide Begin() and End() member functions (and non-member begin() and end() overloads) that return random access iterators into the string (they return pointers, wchar_t const*, and pointers are valid random access iterators). You can use these iterators with any of the C++ Standard Library algorithms that take random access iterators and do not attempt to mutate the underlying sequence. For example, consider using std::find to find the index of the first occurrence of a character.
If you need to mutate a string, use std::wstring or std::vector<wchar_t>. Ideally, consider using the C++ std::wstring as much as possible in your program and only use the C++/CX Platform::String where you need to interoperate with other Windows Runtime components (i.e., across the ABI boundary).