Your Mirage engine has two O2 sensors, as I recall, one before the cat and
one after. This is what the second wire should be connected to. It MIGHT be
the cause of the bogging down.

That  is, the 2nd O2 circuit is open, and the ECU is getting no signal. What
this will do the the ECU operation is unclear: most likely the ECU will
revert to basic mode (ie the engine will run, and typically use more fuel
... its equivalent to what happens when the engine is started with a reset
ECU). In any case, the ECU should be reporting an error code that the rear
O2 sensor is faulty. It may be reporting more errors too. Your 93 harness is
OBD-1, the 96 ECU is OBD2, and the diagnostic connectors are different.

Alternatively the engine may be running very lean: a high operating
temperature is the common symptom. You should be able to touch a hot intake
manifold for about 5 seconds: if its too hot to touch, the engine is running
hot.

The Check engine light should be on. If it's not, verify that
a) the CEL bulb is functional; and
b) your wiring mods are correct and complete. You should have made up a
comparison table of the wiring mods needed by comparing the 93 ECU and 96
ECU connection schematics. You would have noticed in doing this that there
was a second O2 sensor. I suspect you have something other than the missing
O2 sensor wrong or missing.

The rear O2 sensor is quite expensive new, and is AFAIK a 3 wire heated
type. You could probably fool the ECU by providing a resistor network and an
approx sensor voltage, to check if the bog down is related. You could try to
source a rear sensor from a 94-96 4G15 or 4G93 at your local wrecker.

Since the engine will run quite happily (if ineffeciently) in basic mode,
I'd first check ECU error codes, look for damaged vacuum hoses, verify the
cam belt alignment and timing, and the fuel supply.

When was the last time you changed the fuel filter? If not that I'd
suspect the fuel pump.