Is the covid vaccine working to stop the pandemic?

Yes, it is working.

It helps to look at the first country that has essentially achieved 100% vaccination rate, at least for the first dose.

https://www.worldometers.info/coronavirus/country/...

Look how drastically the number of cases has dropped; they went from over 8000 cases per day (over a 7 days moving average) in mid-January to less than 350 today (still on the 7 day moving average).

Death went from 65 per day to 8 today.

Not a decisive factor as yet. Any let up on the vaccination rate would mean that all that effort so far would be wasted. 

We will see after a sufficient percentage of people are vaccinated.  The variants are somewhat concerning.  

Every vaccinated person is one less person COVID-19 can infect and thus pass on to some other unvaccinated person.

Joes plan is working