My selection sort implementation
Here's what I would add if I were doing this as a peer review.

Nested For Loops:

Nested for loops are hard to read. As an alternative, split the nested loop into a separate, aptly named function, if possible. Perhaps a function that returns the next item to be swapped with? You would take your nested for loop and move it to a function that would return what is currently temp if it is there. Then, if there was a return value, you would swap the values. You could even destructure them instead of storing the previous value in a temporary variable: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Operators/Destructuring_assignment

Also, by moving the for loop into a different function, you only have to do this numArray[i] = MIN; if necessary. 

Naming:

Your variables are lowercase, lower_case, camelCase, and UPPERCASE. I suggest standardizing on one. For one thing, MIN looks like a constant to me (from a PHP background), but it is being changed every time in the for loop. Also, what about improving the names: totalNum is unclear to me. Without looking beyond the naming is that an accumulator that stores the sum of all the items? temp could be previousItem.

Other Items:


It's typically recommended to declare variables at the top of the function. j is declared numerous times. 
You initialize MIN at 0, but then reset it inside of the for loop. Why not just declare MIN and not set a value.


A completely different approach:

Finally, I wondered about using Javascript's Array.forEach(). The following is a completely different perspective, but I thought I would throw it out there for you to consider:



selectionSort();

function selectionSort(){
    var originalArray = [4, 34, 2, 5, 12],
        sortedArray = [],
        lowerSortedIndex;
 
  
  originalArray.forEach(function(item) {
    // Arrow function with implied return:
    lowerSortedIndex = sortedArray.findIndex((nextItem) =&gt; nextItem &gt;= item);
    
    if (lowerSortedIndex &gt;= 0) {
      sortedArray.splice(lowerSortedIndex, 0, item);
    } else {
      sortedArray[sortedArray.length] = item;
    }
  });

    console.log(sortedArray);
}




The arrow function could be re-written as:
function(nextItem) { return nextItem &gt;= item; })

I wrote it here if you want to play with it: http://codepen.io/bassplayer7/pen/oBxmbW