I don't think you can control the depth of normal projected views, but you can for section views. So one thing you could do is create a section view from off the part so it is essentially a projected view, then set the section depth shot enough to exclude the opposite side. Then you can hide the section line and view label.
Keep in mind though that this might confuse someone reading the print because they might think that the hole is not supposed to show if they look at the part from that end. Instead of trying to hide the features in the back I'd recommend using a section view from the middle facing outward to show the features on only one side. Then it will be clear to anyone reading the print which features are shown in the view.
You can do what Jamil suggested and then right click on the section line and select "Hide Cutting Line". You can do the same for the note (SECTION A-A). Then, add a new note under the view as shown below.
If you want to show the section line again (if you want to edit it, or for any other reason), you can right click on the section view (side view) and select "Show Cutting Line".