Calculate sum of digits from a given number using String's slice method
Poor testing and vetting

There are a few problems with your approch.


Throwing an error seems to me to be the incorrect response. If the argument it not a number then the result should be NaN. Saves you having to wrap the function in a try catch which will basically stop the javascript engine from optimising the code.
Slice is a little over kill. You can use direct indexing str[index] or via str.charAt(index).
You had parseInt, which will remove any numbers after the decimal point. Use type coercion +num to convert from string to number and ""+num to convert to string.
You don't vet for exponent notation 123e-20
You don't vet - out of the number string and +,or  .
And your testing is very poor.


Rewrite

Below is a rewrite. It fails one test calcCheckSum("0006") should return NaN but it does not which means that isNaN("0006") is failing. This was a surprise to me and I can not make a decision on what to do untill I work out the extent of this bug.



 function calcCheckSum (num) {
    var ret, i;
    if (isNaN(num) || num === "") { // Could be a string that is a number. No need to check if its a type number
                                    // Why throw this will stop the whole program. Return a value that reflects the input
        return NaN;
    }
    // what about negatives,pluses, decimal points, exponent notation, fractions????
    num = (""+num).replace(/\+|\-|\./g,""); // remove junk if any
    if(num.indexOf("e") &gt; -1){  // if exponent then remove it
        num = num.split("e")[0];
    }
    
    ret = 0;
    for (i = 0; i &lt; num.length; i ++) {  // simpler as no need to -1 each iteration
        ret += +num[i];  // + does the type conversion. Split is expensive so just lookup char by index
    }
    return ret;
}

// -- TESTS -----------
var fails = [];
var valuesToReturnNAN = [NaN,"0006","a","0xff","","+",".","-","-0-","-.38.",true,false,Infinity,-Infinity];
var valuesToReturn6 = [123,6,1.23e20,1.23e-20,111111,"123","6","+6","-6","-.6","111111","111.111",".123",.123,0.123,123.,-123,-.123,+123.,+123.0,-123.0,0.123,"0.12300"];
valuesToReturnNAN.forEach(v=&gt;{
    if( ! isNaN(calcCheckSum(v)) ){
        fails.push("failed : " +(typeof v) + " : (" + v + ") did not return NaN");
    }
});
valuesToReturn6.forEach(v=&gt;{
    if( calcCheckSum(v) !== 6 ){
        fails.push("failed : " +(typeof v) + " : (" + v + ") did not return 6");
    }
});
console.log("Failed "+fails.length + " tests.");
fails.forEach(str=&gt;console.log(str));