Reading a CSV file containing a dataset of 8×8 images
Outline

Data and Main aren't exactly helpful class names.  I suggest ImageMatrix and ImageMatrixDB.

In some sense, your code is incomplete, because it just prints the data that it read.  To make this code useful, you would have to offer a way to retrieve the data — and not just by directly accessing dataSetList and dataArray, which should have been private.  I suggest the an outline like this:

ImageMatrix.java

public class ImageMatrix {
    public ImageMatrix(int[] data, int classCode) {
        assert data.length == 64;
        …
    }

    public int[] getData() {
        …
    }

    public int getClassCode() {
        …
    }
}


ImageMatrixDB.java

public class ImageMatrixDB implements Iterable&lt;ImageMatrix&gt; {
    private List&lt;ImageMatrix&gt; list = new ArrayList&lt;&gt;;

    public static ImageMatrixDB load(File f) throws IOException {
        …
    }

    public Iterator&lt;ImageMatrix&gt; iterator() {
        return this.list.iterator();
    }
}


Why are you storing the same data twice, in both dataSetList and dataArray?  You should drop the dataArray, which relies on the magic number 2810.

The file parameter should be a File rather than a String, so as not to give the impression that you it accepts the contents of the file rather than the name of the file.

The parsing routine needs a way to report failure to its caller.  No, printing an error message doesn't count, as the caller would still proceed obliviously.

Implementation

Why are you using a Scanner?  The BufferedReader already has a readLine() method that does what you want.  Note that you fail to close the FileReader, BufferedReader, and the Scanner.

In the Data object, the dataSet array has 65 elements: the 64 data points and the class code.  The class code has no business being part of that array.

public static ImageMatrixDB load(File f) throws IOException {
    ImageMatrixDB result = new ImageMatrixDB();
    try (FileReader fr = new FileReader(f);
         BufferedReader br = new BufferedReader(fr)) {
        for (String line; null != (line = br.readLine()); ) {
            int lastComma = line.lastIndexOf(',');
            int classCode = Integer.parseInt(line.substring(1 + lastComma));
            int[] data = Arrays.stream(line.substring(0, lastComma).split(","))
                               .mapToInt(Integer::parseInt)
                               .toArray();
            result.list.add(new ImageMatrix(data, classCode));
        }
    }
    return result;
}