A carb problem.
1st, on the outside of the carb there will be a Philips screw with a big visible spring around it, this is an air mixture screw, turning it left or right will up and down the idle of the bike by really small amounts. Turn it right by 1/4 a turn and wait a min for the bike to react, if the revs rise a little without the bike being too reved up, it should idle. If it dies straight away try turning to the left 1/4 turn and wait for a reaction. Always remember where the screw was set at before you start turning it. If this doesn't make the bike idle probably you will have to clean the carb.
Inside the carb there are 3 jets you have to clean spotless,,,, idle jet,,,,pilot jet,,,,and main jet. Obviously the idle jet is for idling and starting,,,,pilot jet is for throttle from idle to nearly 1/2 throttle and main jet is from half to full throttle. This is a rough explanation but that's what there for. Every bit of inside the carb needs to be really clean.
The fact your bike dies coming to a stop, then hard to start, then won't take throttle to let you pull away tells me it's your jets BUT it's definitely worth a try first with the air screw, you might get lucky,,,,, maybe it was never adjusted from factory settings and after all the years it needs to be tweaked.
Google carb cleaning before you touch the card and it's delicate setting
Best of luck
2 Wheels's post in Yamaha SR 125 2003 cutting out in first/idle was marked as the answer