I have produced my own fingerless gloves by cutting the fingers off three different pairs with varying degrees of success.
The first pair was a 3mm pair and I cut them down fairly close to where the finger joins the main part. Over time the cut frayed and stretched so more and more water started coming in however, even when they were on the verge of falling apart, my palms were still noticeably warmer than my fingers. I know this because on more than one occasion I took my gloves off underwater and my palms immediately went as numb as my fingers. How could they have gone numb unless they were [relatively] warm before?
The second pair was another 3mm but this time I cut further up along the finger and used Aquaseal to seal the edges of the cuts. I haven't been using these as long as the first but they seem to have more or less the same effect. Some water does leak in through the fingers but I find that if I limit my hand movements this is minimized. I definitely notice a difference when I dive without them compared to when I dive with them.
The third pair is a 5mm pair which I made at the same time as the second. I made sure that they were very tight and cut high up on the fingers. I also Aquasealed the edges to prevent fraying. It might be because this pair is tighter than the 3mm pair or maybe the extra neoprene thickness means it is less stretchy but far less water seeps in through the fingers.
In summary, although it seems counter-intuitive cutting up a pair of gloves to make your own fingerless ones WILL work if you do it properly. I recommend buying 2 or 3 cheap pairs (the 3mm pairs I bought cost less than half of the 5mm pair) and experimenting with different placement of the cuts. Also try using Aquaseal and see if that helps make a seal around your fingers. You won't be able to stop water coming in entirely but you can eliminate some of it. Give it a try, if you buy cheap gloves you have nothing to lose except a few joules of energy in the form of body heat.