First, I have looked on GamersGate, but no one appeared to have the correct answer for my problem, though others have had this problem too.

I have been given a copy of GTA SA from GamersGate and it is being problematic on my computer since the game stutters (the screen stops for half a second or so, whilst all sounds continue). I really like GTA SA and really wish this would work well so that I can put the disk safely away.
I also have the game on disk which is running fine, on max settings. The only time it stutters is in the woodlands with the draw distance all the way up.
The GG version is running currently in 800x600x32 and is a pain to play even then.

The problem with the download version is that the screen stops momentarily every few seconds and there appears to be no reason for this slow down. It can happen in large built up areas or even on CJ's own street. The game is playing and then I get the jolt.
It is very distracting as it can happen every few seconds to every few minutes, quite randomly and very jarring for me. Breaking my immersion, and rather killing the game for me.
The stutters have been noted on several other sites by other people even in the Steam version.

-I have tried adjusting all of the games internal settings so they are well below what the CD version is running at. (currently 800x600x32, 1 draw, frame limiter on, widescreen off, fx quality low, mip mapping off and anti aliasing off).
-I have uninstalled and reinstalled the game.
-I even uninstalled the CD version so that it would not have any possibility to get mixed up.
-Reinstalled the CD version and copied all of the files over from the GG version.
-Reinstalled the CD version copied all of its files over onto the GG version.
-I have updated my video and sound cards in the last fortnight.
-Windows 7 is up to date.
-I have run CCleaner, defragged the entire computer and run a virus scan.
-Reinstalled DirectX 9c
-Run with Admin status
-Changed the comparability to XP SP3 (no change)
XP SP2 (Crashed the game), 98/ME (Wanted me to reactivate the game - then crashed)
Run in 256 colours (no change), Disable visual themes (no change), Disable desktop (no change), Disable Display scaling (no change).
-Disabled my antivirus
-Disabled the firewall
I tried several mixes of the above and they all fail.

This is driving me crazy. I will be sending off a question to Rockstar help desk after here, but given the fact they hate communicating with the outside world they probably will have no interest in helping me.
GG community appear to be stuck on this as well.
So I am asking here as I know people try to help out around here.

Below are Specky results of my system, so you can see I am well in excess of what is needed. Or if someone can spot a know comparability issue.

Sounds similar to the random lag problem I had with SR3 - see if the soluton is of any use!
http://www.gog.com/forum/general/saints_row_3_lag_anyone_got_a_solution

Try setting the processor affinity for the game's executable to a single core. Many older games have issues on newer multi-core processor systems and setting the game to run on a single core only will (usually) eliminate those issues.

The frame limiter makes no difference here.
Have tried the CD version with all the GG files copied over it and it runs without any issues. Running with full draw distance, very high detail, wide screen and at the 1200x800x32. Thanks for the idea, had not thought of that one.

Gave it a try. With the game running individually on separate cores it still behaved the same.
No change, even when I tried duel coring the game.
Thank-you though. Tried deleting the .set file, no change.

After having tried the CD version over the GG files and it working perfectly fine, I do infact believe it to be an issue with the gta_sa.exe that GG install.

Thank-you for the link. I put my machine on to high performance, made sure everything was ready and ran the game. Unfortunately the same problem persists.

Sorry - I forgot there were two solutions in the same comment there. It's specifically this that worked:
"You could also try putting the Saints Row 3 exe file into the DEP setting.

To do this go to Control Panel > System > Advanced System Settings (Top Left, bottom of list)

Next Window should show advanced tab

Click settings beside the performance then next window click Data Execution Prevention tab.

Click turn on DEP for all programs above the window, then at the bottom browse to the Saints Row exe file (There will be 2) one for DX9 and one for DX11, add them both and then click Apply.

Games in Steam are in the Steam directory in common"

Or did you try that as well (the blood is not reaching my brain today!)?

No luck unfortunately. I really think it is the GG setup that has the issue.

Gutted!
Sorry I couldnt be of more help!

First - I would like to thank everyone in this thread, the guys at GamersGate and Mathew at Rockstar support for all their help.
Second - After 4 months of on and off fiddling I succumb to the problem and just went with the simple fix. I found a cracked copy of the games disk version .exe file and copied that into the GTA SA folder. Works like a charm.
I can only hope that when GOG get permission to sell GTA games they can do a better fix job on the installer, the secureROM is the problem. Something in it is eating up processing power doing something rather retarded. As you gave me the idea you get the vote as complete so I can sleep easy knowing this question is 'answered'.

I have read that SecuROM could be rather problematic, even slowing down games (like in Crysis), but it seems that's all true... Incredible, such a nasty DRM is still used... :(

Thanks! Glad You've got it sorted out and can enjoy the game!;)

Wasn't the main reason why CDPR released Witcher (or was it Witcher 2?) DRM-free because many people had massive performance problems due to the DRM those games had at first?

You mention Crysis performance being worse due to SecuROM... does that apply also to Steam and Origin versions of the game?

Can't speak to the origin version, but the steam version has securerom (50 install limit) and the performance seemed fine to me.