What will be the performance penalties of increasing the wing area of a delta winged aircraft to obtain a lower approach speed? Delta winged aircraft such as the Dassault Mirage III have an approach speed of 170 knots as specified by the manufacturer. 

The Mirage F1 was designed to have a lower take off and landing speed than the Mirage III, what would it have taken to reduce the Mirage III landing speed to 135 knots by increasing wing area and reducing wing loading, and installing the F1 engine, and adding leading edge extensions (without adding canards)? 

Could this be done by reducing maximum speed to say Mach 1.4 instead of Mach 2 without sacrificing climb performance?

Some figures:
Mirage III
Thrust: 60.8 kN
Rate of climb: 83 m/s (16,300 ft/min)
Wing Loading:274 kg / sq m

Mirage F1
Thrust: 70.6 kN
Rate of climb: 243 m/s (47,835 ft/min) at high altitude

There is a formula relating change in stall speed to weight of aircraft, not sure if it is applicable here.
What you describe would probably work. In fact rate of climb and operational ceiling would improve. So too would maximum payload. But Mach 1.4 would have been a bad joke.

But your question reads a bit like "How can we improve on the Mirage III wing without doing all the things that were subsequently done to improve on it?"

One approach taken on the contemporary Convair deltas; F-102, F-106 and B-58, was to apply leading-edge camber with a conical profile, apex at the root and widening towards the tip. Developed by NASA, the technique significantly improved low-speed handling and, because it was designed to stay within the root shock cone, had surprisingly little effect at supersonic speeds. The second two designs were both capable of Mach 2. Even the F-102 just about reached your Mach 1.4, despite poor area ruling.