Does saving the game remove your wanted level in GTA III?
Saving at the safehouse and then loading this save will clear wanted level.
The Grand Theft Auto wiki page for Grand Theft Auto III lists various ways on how to reduce wanted levels, including the state of using safehouses.
One of them is indeed using the save point, however this is from GTA Vice City and onwards. Since GTA III was released before, it would seem that reducing wanted levels in this game won't work.