my heater core has a water valve on it, what would happen if i put a heater core with out the valve in?

First thing is the water valve part of the heater core or a separate device? I f it is part of the heater core and you replace it with a core that has no valve then when you turn on your A/C you will not get the cooling you are expecting.

also it's what they call a mixing valve if it's not opening your not going to get heat

Cars that I have expereince with use a blend door to mix cold air with the hot air from the heater core to control the temperature of the air entering the cabin. Sound like from what you are saying that Mistsubishi is using water flow from the mixing valve to do the temperature control. Without this valve inline you would have unbearable heat coming from the heater when everything gets warmed up. If you can live with turning the blower motor off and on all the time or riding with the windows down you might get by with a heater core that does not have the mixing valve if you can find one with the proper dimensions and the correct inlet/outlet tube configuration. Probably not going to be an easy task.

the mixing valve i'm reffering to is between the waterpump and the heater core. don't know if your car has this but usually runs off vacuume to open so it lets the water through so you get heat.