Is it normal for a new clutch to grind trying to get into 1st gear while dieting to a stop?

What's grinding?

The clutch or the transmission?

I never heard of a clutch or transmission dieting.

This is a problem when you diet to a stop.  You are a fool of you buy without an independent mechanic checking the vehicle.

Youi never shift back into first gear.You only use first gear to start driving.You can shift back into 3rd or 2nd but never into first.If you do your gears will always grind.

If everything else is okay with the clutch and transmission, don't shift into first unless you are stopped.  Problem solved.  

HHR--one of the biggest POS Chevrolet ever produced.

THE CLUTCH DOESN'T GRIND dumbass, the gears do. That is often an indication that the clutch is not fully disengaging when the pedal is pushed in, or the synchromesh isn't working. Unless you have the skill to properly diagnose it...RUN 

A  used Chevy HHR.  That is all you need to know.  Stay away.

You didn’t mention the make and model.

But with a huge number of manual transmission designs, 1st gear is *ONLY* ever meant to be engaged when the vehicle is at a full stop; if you’re already rolling you pull away in 2nd, and on cars with high torque engines it’s normal to pull away from a dead stop in second retaining 1st for hill starts and/or heavy loads. So as that means it does not need synchromesh, it often doesn’t have synchromesh. That’s not just a cost saving issue, it makes 1st gear much tougher and with fewer parts it’s another improvement in reliability. Reverse never has synchromesh for the same reasons, and in addition usually has noisier but immensely stronger straight-cut gear teeth. Many manual transmission designs also have straight cut gear teeth for 1st gear but that’s less common.

More recent manual transmission designs on upmarket models tend to have both synchromesh and helical-cut gear teeth for 1st gear.

Your old clutch was worn and slipping, so that made it possible to engage first gear without grinding.

The clutch pedal should disengage 2" off the floor. There may be air in the clutch hydraulic system. If it grinds as you say it's either because the  clutch pressure plate is warped or there may be a bushing in the flywheel that the transmission input shaft rides in that is bad causing the transmission input shaft to keep spinning when the clutch pedal is all the way down to the floor. Not a very good vehicle to purchase from a mechanical view and repairs that are common.

Sounds very much like the syncromesh on first gear is shot.  It will get worse and gearbox repair/replacement will be eye watering. Walk away.