Not only can you do that I recommend it. When you put an IR filter on the sensor you lose control. There's various IR filters that can be applied to the front of the lens to give various different effects. Not only that, but with the IR filter on the front of your lens your autofocus system remains intact despite the fact that IR bends through the lens at a different angle than visible light.
The downside is you can't see what you're doing through your shutter, and the D70 doesn't have lifeview.
That said it's not quite as simple as removing the hotmirror. Without looking at it if there's any thickness to it at all it may bend the light hitting the sensor. This is typically not so much an issue on a DSLR as a Point and shoot where the rear element of the lens is closer to the sensor but you need to be aware that there's a potential to firstly screw up the focus to the point where lenses can't focus at infinity and you also expose the sensor to potentially getting dust (much more serious then simply wiping it off like if you get dust on it now.
The better solution is to either remove the IR coating from the hot mirror with a really REALLY fine cutting compound (such as car finishing polish) or to replace it with an appropriate size and thickness piece of glass.