简单粗暴，直接上代码！！！（3.23的API）
补充：https://github.com/shaoms/ArcGIS-API-for-JavaScript/tree/master/Print 这里面有我写的4.xapi打印功能
<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8">
<meta name="viewport" content="initial-scale=1, maximum-scale=1, user-scalable=no">
<title>地图打印</title>
<link rel="stylesheet" href="https://js.arcgis.com/3.23/dijit/themes/claro/claro.css">
<link rel="stylesheet" href="https://js.arcgis.com/3.23/esri/css/esri.css">
<script src="https://js.arcgis.com/3.23/"></script>
<link rel="stylesheet" type="text/css" href="../css/mystyle.css" />
<script>
require([
"esri/layers/ArcGISDynamicMapServiceLayer",
"esri/map","esri/config",
"esri/tasks/PrintTask",
"esri/tasks/PrintTemplate",
"esri/tasks/PrintParameters",
"dojo/domReady!"
], function(ArcGISDynamicMapServiceLayer, Map, esriConfig, PrintTask, PrintTemplate, PrintParameters){
var lyr = new ArcGISDynamicMapServiceLayer( "https://sms.esrichina.com/server/rest/services/test/22/MapServer");
var mymap = new Map("viewDiv", {
basemap: "osm",
zoom: 9,
center: [116.402544,39.915378]
});
mymap.addLayer(lyr);
var button = document.getElementById("button");
button.onclick = function(){
var printTask = new PrintTask("https://sms.esrichina.com:6443/arcgis/rest/services/Utilities/PrintingTools/GPServer/Export%20Web%20Map%20Task");
var template = new PrintTemplate();
template.exportOptions = {
width: 800,
height: 600,
dpi: 96
};
template.format = "PDF";
template.layout = "A3 Portrait";
template.preserveScale = false;
var params = new PrintParameters();
params.map = mymap;
params.template = template;
printTask.execute(params, function(evt){
console.log(evt);
window.open(evt.url,"_blank"); //在新的标签页打开打印连接
});
}
});
</script>
</head>
<body>
<div id="viewDiv"></div>
<button id="button" title="打印">打印</button>
</body>
</html> 值得注意的是打印的地图服务需要公有的（共享给everyone），因为通过打印服务工具来间接访问地图服务时，需要用token，此token都是通过map中服务的token直接传递过来。你也可以打印包含受保护服务的地图，详细操作见下面的连接：
http://enterprise.arcgis.com/zh-cn/server/10.3/create-web-apps/windows/printing-maps-that-contain-secured-services.htm