You need some more return statements before calling the same function again.

And while you return for every true if statement, you could omit else.

function arrsort(arr) {
    return arr.sort(function(a, b) {
        return a - b;
    });
}

const binarySearch = (arr, num, start, end) => {
    arr = arrsort(arr);
    start = 0;
    end = arr.length;
    var mid = Math.floor(end / 2);
    if (arr[mid] === num) {
        return true;
    } 
    if (arr[mid] < num && end > 1) {
        return binarySearch(arr.splice(mid, Number.MAX_VALUE), num, start, end);
    } 
    if (arr[mid] > num && end > 1) {
        return binarySearch(arr.splice(start, mid), num, start, end);
    } 
    return false;
}