Make iPhone use GPS-only location services The question is as simple and clear as it sounds.

When celullar data and Wi-Fi are turned off on my iPhone 6, location services work great and I get my location in a moment with a precision of 1-2 meters. 

However, if I turn my celullar data on, it takes 10-15 seconds to get my location and, usually, it is pretty incorrect (+- 200 meters and it randomly moves around while I am standing at the same place). As some of my friends have the same problem, it looks like it is mobile network operator issue (Altel 4G, Kazakhstan).

Why does iPhone prefer to use cell network-based or wifi-based location services while GPS is doing good? How can I turn off cell network-based and wifi-based location services, so it uses only GPS services and doesn't work at all if GPS is not available.

Now, I have to turn my celullar data off in order to get my precise location and turn it on later. However, it makes playing some games involving both location services and celullar data impossible.
The iPhone's systems are optimized for battery life. From the chip design to the OS, battery conservation takes precedence over all.

GPS chips are massive power consumers. Read these answers for more information on GPS chip power use. Due to this, the iPhone will always prefer to find its location with wifi/cell tower triangulation, then refine with GPS.  The phone will often quickly cycle the GPS chip on and off, confirming location as needed. (remember, computers think in microseconds or smaller)

Since the iPhone is not a dedictaed GPS, you likely will never find a way to force it to become one. You might try an iPhone GPS application, many of which seem to 'force' the GPS chip (and drain the battery).

For more, learn about Assisted GPS, which explains how GPS works on your phone, including iPhone. This may also explain why your carrier might be a challenge, as it might not be providing you with Mobile Station Assisted data.