For added new element into the array, push()push() should be the answer.
For remove element and update state of array, below code works for me. splice(index, 1) can not work.
const [arrayState, setArrayState] = React.useState<any[]>([]);
...
// index is the index for the element you want to remove
const newArrayState = arrayState.filter((value, theIndex) => {return index !== theIndex});
setArrayState(newArrayState);