Converting a CSV File Into a 2D Array

Use String.split() and Array.map()

Because "the map() method creates a new array with the results of calling a provided function on every element in this array" (source: MDN), it is ideally suited somewhat suitable for creating a two dimensional array from a very basic CSV string that has already been converted into an array via the split() method.

function csvToArray (csv) {
    rows = csv.split("\n");

    return rows.map(function (row) {
    	return row.split(",");
    });
};

// Hard-coded for brevity, but you can set this variable with FileReader
var csv = "the,quick,brown,fox\n" +
          "jumps,over,the,lazy,dog";

var array = csvToArray(csv);

console.log(array);

Open your console.

Update:

This basic solution falls apart if your cells contain quotes, commas or other escaped characters. To address more complex CSV strings, you'd have to implement a RegEx solution (see accepted answer to How can I parse a CSV string with Javascript?); and to support multiple common formats, you'd be better off just using a library.

I needed something like this today so I found snippet originally done by by Bennadel and cleaned it up a bit also adding in edge cases.

/*
 *  shortened version of:
 *   http://www.bennadel.com/blog/1504-ask-ben-parsing-csv-strings-with-javascript-exec-regular-expression-command.htm
 *
 *  Supports columns that are quoted/non-quoted. Takes care of quoted columns that may also have \n's inside
 *  them instead of using a naive approach of split('\n')
 *
 *  @param csvString {string} CSV file of rows separated by new lines.  
 *  @param delimiter {string} delimiter used to split columns 
 *
 *  return {rows} Array of rows with columns containing parsed CSV data
 */

function CSVParse(csvString, delimiter = ",") {

  if (!csvString || !csvString.length)
    return [];

  const pattern = new RegExp(
   ( "(\\" + delimiter + "|\\r?\\n|\\r|^)" +
     "(?:\"([^\"]*(?:\"\"[^\"]*)*)\"|" +
     "([^\"\\" + delimiter + "\\r\\n]*))"
   ), "gi"
  );

  let rows = [[]]; 
  let matches = false;

  while (matches = pattern.exec(csvString)) {

    const matched_delimiter = matches[1];
    const matched_cellQuote = matches[2];
    const matched_cellNoQuote = matches[3];

    /*
     * Edge case: Data that starts with a delimiter
     */
    if (matches.index == 0 && matched_delimiter)
      rows[rows.length - 1].push("");

    /*
     * Fix empty lines
     */
    if(!matches[2] && !matches[3])
      continue;

    if (matched_delimiter.length && matched_delimiter !== delimiter)
      rows.push([]);

    const matched_value = (matched_cellQuote)
      ? matched_cellQuote.replace(
          new RegExp("\"\"", "g"), "\""
        )
      : matched_cellNoQuote;

    rows[rows.length - 1].push(matched_value);

   }

   return rows;
}

The logic is similar to (but simpler than) what you're already doing to display the results:

var data = [];
var rows = e.target.result.split("\n");

for (var i = 0; i < rows.length; i++) {
  var cells = rows[i].split(",");
  data.push( cells );
}

var data = [];
var csv = "one,two,three\n" +
          "four,five,six";

var rows = csv.split("\n");

for (var i = 0; i < rows.length; i++) {
  var cells = rows[i].split(",");
  data.push( cells );
}

console.dir(data);