I have always understood that when the beautiful new city of Jerusalem came down from Heaven and our Lord Jesus reigned forever and ever that the murderers, sorcerers, etc. would be gone from the new earth. Please explain this for me.

Thanks for your prayers and encouragement. If your question about the New Jerusalem is in regards to Revelation 22:15, I take that to be a general statement that applies not just to the City but the whole of the earth because of Revelation 21:1-8. I think like you do as you said; “when the beautiful new city of Jerusalem came down from Heaven and our Lord Jesus reigned forever and ever that the murderers, sorcerers, etc. would be gone from the new earth.” Now the 1000 years before that, while the Lord is putting down all rule and authority and power (I Corinthians 15:23-25), then there will still be sinners who upon swift righteous judgment will be “cast alive” in the lake of fire which will be visible on the earth during that time.