2009 Saturn Vue. Rear Wiper and Washer both stopped working at same time.

Replacing parts just to replace them wont fix a bad wire or part. Better to use a voltmeter and ohn meter to check if your getting power to the wires. You may have a bad connection or bad switch on the column for the pumps. Without checking the circuits it will behard to tell what it is thats wrong. Find a wiring diagram and trace the wires and components.

Just replacing parts isn't the way to fix this problem , viewing wiring diagrams too see what all is involved in making the wipers work is . Then using a digital volt ohmmeter to test electrical circuits . Also looking at factory service info. to see how it's suppose to work.
Free wiring diagrams here http://www.bbbind.com/free-tsb/ Enter vehicle info. year , make , model an engine size . Under system click on body & accessories , then under subsystem click on wiper/washer . Click the search button ,then click the blue link. Looking at the wiring diagram i see two fuse's an two relays that are controlled by the BCM - body control module . Also hooking up a scan tool that can read BCM DTC'S - diagnostic trouble codes could be helpful . The wiper switch is a input to the BCM - the BCM will energize the relays to turn on the wipers.

Wiper/Washer System Components
The Wiper/Washer System consists of the following components:
• Windshield wiper/washer switch
• Body control module (BCM)
• Wiper 1 relay
• Wiper 2 relay
• Wiper diode
• Windshield wiper motor
• Windshield washer pump
• Windshield washer nozzles
• Windshield washer solvent container
• Windshield wiper arm and blade assemblies
• Windshield wiper transmission
• WIPER/SW 10A fuse
• WIPER 25A fuse

Wiper/Washer System Description
The body control module (BCM) controls wiper motor low speed operation. The washer pump and high speed operation are controlled directly by the wiper/washer switch. The windshield wiper/washer switch supplies voltage on the signal circuits to the BCM for windshield wiper/washer operation. When WASH, MIST, DELAY, LOW, or HIGH is detected, the BCM energizes the wiper 1 relay by suppling voltage to the relay coil. This allows battery voltage from the WIPER fuse to flow through the relay switched input then through the contacts and out the relay contacts to the wiper 2 relay switch contacts. Since the wiper 2 relay switch contacts are normally closed to the low speed circuit of the windshield wiper motor, the motor will operate at low speed.

DTC B3715 02: Front Wiper Relay Drive Circuit Short to Ground
DTC B3715 05: Front Wiper Relay Drive Circuit Short to Battery or Open

Your windshield wiper's are computer controlled by the BCM - body control module . The wiper switch is an input to the BCM , which energizes two different relay's to turn on the wiper's . Taking the vehicle to a qualied repair shop an having diagnostic's run would be your best bet , unless you have a professional scanner that can read DTC'S - diagnostric trouble code's in the BCM !
DTC B3715 00: Front Wiper Relay Drive Circuit
DTC B3875 00: Wiper High Speed Relay Circuit
DTC B3922 00: Front Wiper Function Select Circuit
This is always the first step in the diagnostic process . An if you do not know how they work ,reading factory service manual info. should be done .
Circuit/System Description
The body control module (BCM) controls the wiper motor based on input from the windshield wiper washer switch. The BCM monitors the wiper washer switch through three separate signal circuits and a ground circuit. The windshield wiper switch high signal circuit is used to determine high speed wiper operation, the windshield wiper switch low signal is used to determine low speed, intermittent, and mist operation through the use of a resistor ladder, and windshield washer switch signal circuit is used to determine washer operation.
Your best bet , take it to a qualified repair shop.

There is a electric motor that pumps washer fluid . Located in the bottom of the washer fluid tank .
Wash Operation (Front and Rear Wipers)
The front and rear washer systems use the same windshield washer fluid pump. When either the front or rear wiper is in the washer position voltage will be supplied to one side of the windshield washer fluid pump (depending on whether it is front or rear), while the other side of the pump is grounded.
At this point, the windshield washer fluid pump sprays solvent onto the windshield. When the front or rear washer is activated, the BCM receives an input from the switch that is activated. The BCM will control the wipers while in the WASH mode. The BCM will control either the front wiper relay or the rear wiper relay to turn on the wipers. The windshield wipers operate at low speed for 3 swipes and returns to the park position.

When turning on the washers do you hear the motor run ? Have some one try it while you listen at the washer fluid tank ! These pump motors do go bad .
turn OFF the ignition.
Disconnect the harness electrical connector of the windshield washer fluid pump.
Connect a test lamp from the windshield washer pump control circuit to a good ground .
Turn ON the ignition, with the engine OFF.
Press the front washer switch.
Does the test lamp illuminate?
YES or NO !

fill the bottle or clean nozzle or replace pump or fuse

check the wiper washer line it could be broke or clogged

unhook the hose at the rear wiper,test, maybe the nozzle is plugged, or hose bent.

wipers and washer should be on the same fuse
could be the switch

if your vue is a newer model it is common for the washer hose to get pinched by the cowl when the hood is shut. This in turn can puncture the hose, which is easily replaceable. if that is not the problem you may have a bad washer pump.

Hi! U need to check the switch and the wiring circuit that controls the motor.