To discourage users from printing reports and dashboards, you can have them subscribe to the reports and dashboards instead. This will email the report or dashboard when the data changes on the report, typically daily or weekly. Select Subscribe in the upper-right corner of the browser. Power BI will read the account you're signed in with and subscribe you using that email address. When subscribing to reports, you must select the report page that you wish to be emailed to you. With dashboards, the entire dashboard will be emailed. 

You can also set up alerts from your mobile device to alert you when a critical number changes on a report. While looking at a dashboard, you can click the alert icon (it looks like a bell) to create an alert. This will monitor the data on the report, and upon that number hitting a certain threshold, it will send you a phone alert and, optionally, an additional email. Alerts are great mechanisms to let you know if a given critical number, such as a profit margin, has fallen. 

Subscriptions and alerts can be managed in the Power BI settings area under the Alerts and Subscriptions tabs. You can turn off alerts and subscriptions here, as well as edit the subscriptions. By default, the frequency of subscriptions will be whenever the data is updated, but this happens typically no more than once per day (although this can be altered).