Assuming this is a Mikuni SBN with high and low mixture adjusters only...
The low speed mixture adjustment screw is for idle mixture. You've confirmed, the accelerator system functions, the accelerator injection nozzle isn't plugged with gum/dirt and produces a strong shot as normal. Idle is good (adjust idle mixture screw, and it works fine)
Assuming you can get past the off idle dead spot and into WOT it's running reasonable, I strongly suspect your low speed bypass (AKA part throttle transition) is clogged or restricted. See the yellow colored lines of this drawing showing the path of this important and difficult to clean circuit.
Also, confirm the size of the low speed jet is the correct factory spec, depending on where/what this carb was off of originally (some other motor?) it may be too small.
And, confirm the high speed check valve isn't damaged, it should lay flat covering the hole in the kidney-shaped metering plate. It's important to use a mikuni piece in this location, not aftermarket.