From the topics I gives in comment, it gives strange result.
And as I don't know if you insist the button be <button> and not a <a>, I created a workaround to make it seems work.
Edited: 
If you want to save Image to server.
Change 
  // Create a hidden link to do the download trick.
  var a =document.createElement("a");
  a.setAttribute("href", image);
  a.setAttribute("download", "canvas.png");
  a.click();    
to 
  var post = new XMLHttpRequest();
  // I assume your web server have a handler to handle any POST request send to 
  // '/receive' in the same domain.
  // Create a POST request to /receive
  post.open("POST", "/receive");
  // Send the image data
  post.send(image);
And you may need some further process at your server side to save the posted data to local file system, like what I did in my node.js server:
// Handle POST from xxx/receive
app.post('/receive', function(request, respond) {
  // The image data will be store here
  var body = '';
  // Target file path
  var filePath = __dirname + '/testWrite/canvas.png';
  // 
  request.on('data', function(data) {
    body += data;
  });
  // When whole image uploaded complete.
  request.on('end', function (){
    // Get rid of the image header as we only need the data parts after it.
    var data = body.replace(/^data:image\/\w+;base64,/, "");
    // Create a buffer and set its encoding to base64
    var buf = new Buffer(data, 'base64');
    // Write
    fs.writeFile(filePath, buf, function(err){
      if (err) throw err
      // Respond to client that the canvas image is saved.
      respond.end();
    });
  });
});
var saveImgae = function() {
    var canvas = document.getElementById("myCanvas");
    var image  = canvas.toDataURL("image/png");
   
  // Create a hidden link to do the download trick.
  var a =document.createElement("a");
  a.setAttribute("href", image);
  a.setAttribute("download", "canvas.png");
  a.click();    
  
  // Not work for me. It download a file , but without file type and filename is simply download, maybe it works for someone.
   //  var image = canvas.toDataURL("image/png").replace("image/png", "image/octet-stream");
  // window.location.href=image; // it will save locally
};
// This is just something like your onclick="saveImage()"
var button = document.querySelector("button");
button.onclick = saveImgae;
// Fakes , I just want to demo the click...
var canvas = document.getElementById("myCanvas");
var context = canvas.getContext("2d");
context.font = "40pt Calibri";
context.fillText("My TEXT!", 50, 100);
context.font = "20pt Calibri";
context.fillStyle = 'red';
context.fillText("Tesr", 50, 200);
<canvas id="myCanvas" width="400" height="200" style=" border:1px solid #d3d3d3;"></canvas>
<button id="save">Save image</button>