I assume GOTY includes all DLC listed in Steam under the DLC pack. The only way I know about to actually "deactivate" a DLC is asking Steam support to permanently remove it from your account without any refunds. So I can only give you a list of the benefits provided by the DLCs here and you have to be honest with yourself to not "use" them, e.g. always consider yourself to be 200k poorer than you are:
- I'll skip the cars and clothes, since they shouldn't be difficult to notice - basically you don't own anything but a motorbike and your own clothes in the beginning
- Police Protection Pack: Apart from the SWAT stuff it adds the "High Speed" mission
- The High Roller Pack: $200k and premature access to the Tuono vehicle and High Roller outfit
- The Red Envelope Pack: those red envelopes scattered around town containing $50k each
- Top Dog Gold Pack / Top Dog Silver Pack: A total of both 8 police abd triad skill points in total
- The Zodiac Tournament: That tournament
So in summary, if you don't want to use the too severe DLC bonuses, don't collect the red envelopes and always leave $200k and 8 triad/police skill point unused...
If you're on PC (or can somehow access the respective files on your console), you can remove the respective files (and probably have to deactivate updates for the game) I found a list of the DLCs' respective filenames here:
1E6323E1.dat Top Dog Gold Pack
576E446C.dat Top Dog Silver Pack
AC8D6F78.dat High Roller Pack
E58008F5.dat Red Envelope Pack
E80C9CFE.dat police protection pack
3E97A062.dat Tactical Soldier Pack
8C79ECFB.dat Retro Triad Pack
67EE992C.dat Martial Arts Pack
81F578F0.dat Dragon Master Pack
613E5E9C.dat Square Enix Character Pack
849D8C70.dat Street Racer Pack
B41D5130.dat Community Gift Pack
BA29F60B.dat Ghost Pig Pack
CD90EBFD.dat Screen Legends Pack
D500D5B5.dat Deep Undercover Pack
F3249186.dat Gangland Style Pack
FD1036BD.dat Valve T-Shirt Pack
779AC7EF.dat SWAT Pack
5AE2D067.dat Drunken Fist Pack
9ADD7588.dat Monkey King Pack
41CADD1F.dat Law Enforcer Pack
28333911.dat Movie Masters Pack
C8F81F7D.dat Triad Enforcer Pack
D3D01205.dat Wheels of Fury
7A1653E4.dat gsp packStory DLC:
E0E8FC75.dat Zodiac Tournament Pack
13EFB7EA.dat Nightmare in North Point