Very possibly the torque converter clutch is engaged and stalling the engine. I'm assuming you have an automatic transmission.
Here's a directory list for you if you want a specialist to look at it:
https://repairpal.com/saturn-repair-in-remus-michigan
RepairPal Certified shops can diagnose and repair your 1993 Saturn SL1. They provide transparent pricing with a minimum 12-month or 12,000-mile warranty on repairs and services.