I thought about putting something about Winslow, AZ in there but getting it in a short clue was hopeless.
OK, let’s try
ART.
- Fleming or Linkletter
- With “F,” it’s a gas!
- With a p, separate
- Paul’s singing partner
- Fine or noble
- Verb in Juliet’s lament
- Science degree alternative
- A Picasso, or a Garfunkel
Good ones all, but I’m going with Wheelz for:
You’re up!
Stole that from the Barenaked Ladies, but I couldn’t resist!
Next up is CHUCK
- Beef shoulder
- Toss
- Word in a tongue-twister, with wood
- Groundhog minus plant material
- Richie’s missing brother
- Ground beef type
- Connors with a rifle
- Jaws of a drill?
- Goes after ground or before roast
OK, time to call it. I was a little disappointed nobody referenced Peanuts 
, but I liked this one, for a use I hadn’t thought of:
You’re up, @SunUp !
This looks fun. Someone needs to post a word, though, for me to join
Thanks, Wheelz!
This time out we’ll try
ORGAN.
Here you go. Looking forward to your clues!
- Instrument heard in church
- Found inside the body
- Type of donor
- Monkey’s grinder
- Heart of the matter?
- Hammond or Casavant
ETA: Welcome to the game, Cardigan!
You can tell spoons has a lot of experience with crossword puzzles. His clues sound more…legitimately crosswordy than mine, at any rate. 
Don’t worry. We’ve all come up with some really good ones and some really… not so good ones.
It’s all for fun. Hope you enjoy yourself here.
- Offal thing
- “96 Tears” feature
- New Mexico mountain range
Wheelz takes it! I’m a sucker for a good pun.
Though I would point out this, Cardigan: Your third clue,
Type of donor
got some bonus points for me because another likely answer, BLOOD, takes up the same number of letters as the actual answer, thus being a vicious sidetrack if the solver goes in the wrong direction before any crossing words are filled in.
OK, Wheelz, you’re up!
Thanks, SunUp!
Let’s see what we can do with
DREAM
- Gaiman’s Morpheus
- Everly Brothers’ task
- Type of sicle