Is there way to turn-off auto-tagging of enemies in Far Cry 3's minimap?

As of patch 1.04, as you found out, you can turn Weapon Taggingon/off in the settings, but not the minimap itself, or the radar function.

You can turn off the HUD completely, or turn some elements by applying some unsupported patches to your game. I know, this is not what you asked, but there seems no other way.

This guide explains how you can apply changes manually.

This forum thread lists some of these community patches. Beware, you might be kicked/banned from Multiplayer games if you play it with these on, so, make a backup of what you are overwriting.

UPDATE: The above mentioned patch files are apparently no longer hosted due-to copyright violations.

UPDATE 2: You can download the patch (for version 1.04) that removes the enemies from the mini-map here.

This forum post, "How to remove the wallhack tagging when using the camera" from the Ubisoft forums, describes a method to disable "wall hack tagging" (seeing tagged enemies through walls):

Open the FC3.dll and/or FC3_d3d11.dll (depending on what you use) in any hex editor.
Search for the following hex array:
53 68 6F 77 54 68 72 6F 75 67 68 57 61 6C 6C 73 41 6C 70 68 61

Change the last value from 61 to 6F, so it reads like so:
53 68 6F 77 54 68 72 6F 75 67 68 57 61 6C 6C 73 41 6C 70 68 6F

Lastly, do a search for the following array:
53 68 6F 77 54 68 72 6F 75 67 68 57 61 6C 6C 73 00

Change the second to last value from 73 to 6F, so it reads like so:
53 68 6F 77 54 68 72 6F 75 67 68 57 61 6C 6C 6F 00

Essentially, you're renaming the commands ShowThroughWallsAlpha to ShowThroughWallsAlpho and ShowThroughWalls to ShowThroughWallo, which nullfies the commands when they're called.

For hex editors, see: https://superuser.com/questions/14465/hex-editors-for-windows

There is also a mod here that claims to remove wall hack tagging.

I found those from this thread, "Mods for Far Cry 3", in the Ubisoft forums. There are also a couple of mods or compilation mods (like this one) there that have a feature of removing the mini-map or enemy positions in the mini-map.

From the Far Cry Nexus, the mod, HUD annoyances fixed, claims to remove enemy icons on the mini-map:

This mod currently replaces the textures used for the minimap elements and the camera HUD elements in order to improve gameplay and/or remove distracting visual elements. The minimap remains intact because I think functionally it is fine, but I have removed the icons for collectables and enemies from displaying, so that more exploration is needed.

Also from the FC Nexus, there are compilation mods (includes many features) that will either remove wall hack tagging or disable or change the minimap to not include tagged enemies:

Greetings to Malmo
Legit Far Cry
Ziggys Mod
Poor BastUrd
Sleepingwsirens Modpack ReDux