Yes, you can buy all the electronic parts by themselves, but given that the electronic parts are the bulk of the cost, you may not save much.
The MINDSTORMS EV3 set (MSRP $349.99 USD) contains:
1 - EV3 Intelligent Brick (MSRP $189.99 USD)
1 - EV3 Color Sensor (MSRP $39.99 USD)
1 - EV3 Infrared Sensor (MSRP $29.99 USD)
1 - EV3 Touch Sensor (MSRP $19.99 USD)
1 - EV3 Cable Pack (MSRP $14.99 USD)
2 - EV3 Large Servo Motor (MSRP $24.99 USD each)
1 - EV3 Medium Servo Motor (MSRP $19.99 USD)
1 - EV3 Infrared Beacon (MSRP $29.99 USD)
- Software: Free download.
That comes to a total of: $394.91, or $44.92 over the price of the whole kit.
That means you would have to find these pieces for a fair bit less than the MSRP to save any money (remember shipping costs if you get them from multiple sellers), which could be difficult as these pieces tend to have good resale value. At quick glance on BrickLink, I found you can maybe get $40 of an EV3 Intelligent Brick, but the EV3 Medium Servo Motor is actually selling over the MSRP (possibly because it is backordered).
We don't need anymore lego bricks
The Mindstorms kits actually come with LEGO Technic pieces, not bricks. You would not really be able to use these electronic parts without a fair number of Technic pieces.
If you plan to follow along with the instructions from the kit, you would need to have the parts in the kit.