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...