should i cut a city from my itinerary or re-arrange them? (15 day trip)

Are you stuck with having to fly in/out from Barcelona?

If I were trying to do your destinations in the allotted time I would book a multi-city ( aka open jaw) ticket into Barcelona and home from Madrid. After doing Barcelona , fly to Seville, and then train the rest of the way to Madrid

If r/t in/out of Barcelona is carved in stone, how you order the destinations, in my view, is just a matter of choosing which color rope you want the hangman to use

My $0.02

Happy travels

Don’t cut any time from Madrid! That would be a huge mistake! In fact, maybe cut some time from Barcelona. Stay nearby in the wonderful and scenic Costa Brava ( look at Begur) for a few days.

Cut a city? I would add two maybe three.
Arrive in Barcelona (3 nights)
Train to Madrid (Day trip to Toledo and maybe another to Segovia. 4 nights)
Train to Cordoba. (2 nights)
Train to Sevilla. (3 nights)
Train to Granada. (2 nights)
Fly to Barcelona. (1 night) Stay at a hotel near the airport for your next day travel home.

I should mention, I don't like to travel this way - it's more like a scavenger hunt than a cultural experience. Too much time "getting there" and not enough time "being there".
If this style of travel appeals to you, dedicate yourself to in-depth planning to maximize your days. Reservations are a must in many locations.

This is a hectic pace but you see many of Spain's best while leaving numerous gems for your next Spanish adventure. Trust me, you will be back.....and we haven't even mentioned Portugal.

I would schedule three nights in a charming town mid trip. But that's me, city city city city not my ideal itinerary.

Take a day from Granada and add one to Seville.

I agree with shifting a night from Granada to Seville--not because Granada isn't worth 3 nights, but because Seville is a great deal larger, with more widely scattered sights, and really needs 4 nights. In the unlikely event you get antsy while you're in Seville, you can consider a day trip to Cordoba (though a last-minute train ticket will probably not exactly be cheap). Cordoba is a great city, and I'd push you to include it if you had more time.

As hinted above, there are sights in many of your cities for which you'll need to buy tickets in advance. Failure to do that will lead to way too much time spent in ticket lines or even failure to get inside at all.

Job #1 is securing your ticket for the Alhambra. It sells out early. If Alhambra General tickets are sold out, try for the Dobla de Oro ticket. If those, too, are sold out, see whether the Granada Card has Alhambra slots available on the days you'd be in town. If necessary, you can reverse the southern part of your itinerary and travel Barcelona-Seville-Granada-Madrid-Barcelona. Or even Barcelona-Madrid-Seville-Granada-Barcelona. Those two options would push Granada a bit later and might make it easier to get an Alhambra ticket.

For Barcelona you need to purchase tickets in advance for any of the following sights you want to see: La Sagrada Familia, Parc Guell, Casa Mila/La Pedrera, Casa Batllo, Picasso Museum, and Palau de la Musica Catalana. The first five have horrible lines. The last sometimes runs out of space on its English-language tours.

In Seville you should buy your Alcazar ticket in advance because of the long, outdoor ticket line. The same situation exists at the Cathedral, but you can circumvent that line by getting a combo ticket at the nearby Church of El Salvador. (This is Rick's very useful tip.)

In Madrid some folks have been happy to have purchased a ticket to the Royal Palace in advance, because they saw a ticket line. It is a popular sight, including with Spaniards. I suspect it may be busier on weekends and holidays, but that is only a guess. Some folks suggest pre-purchasing a ticket to the Prado as well. I had no ticketing issues in Madrid, but I was there in 2016, and there are more people traveling these days.

geovagriffith is right

Can you make a list of what you want to do in each city and then see how many days each city requires?

If you have to fly roundtrip to Barcelona, why not put all your nights in Barcelona at the end, instead of splitting your time in Barcelona, with some nights at the beginning and more nights at the end? Have you bought plane tickets yet? If you arrive in Barcelona early enough in the day, can you go in this order:

take the train to Madrid and spend your first nights in Madrid, then Seville, then Granada, ending in Barcelona?

OR, the day you arrive in Granada, train and/or buses/and/or plane to Granada, 2 nights in Granada, then Seville-Madrid-Barcelona?

OR: the day you arrive in Granada, train and/or buses/and/or plane to Seville, then Granada, then Madrid, then Barcelona?

Can you fly to Madrid, and depart from Barcelona, or the reverse, fly to Barcelona, fly from Madrid?

Or possibly: Fly to Seville, then Granada, Madrid, the fly back from Barcelona?
OR possibly: Fly to Seville, then Granada, Barcelona, then fly back from Madrid?

See which itinerary has the best combination of price versus total trip duration versus times you arrive and depart.

Everyone has personal opinions about those cities. It's hard to give advice without knowing your interests and your travel style (basically speedy or laid-back). I'd encourage you to read a good guide book and try to get an idea of what you most want to see and do in each place.

My other advice is to make your decisions really fast, unless you are planning to travel light and stay in youth hostels (never done that in Spain). Train tickets for April are probably on sale already and the prices go up as time passes. That's a popular time to visit (right after Easter) and the longer you wait the harder it will be to find hotel rooms in good locations at good prices.

Don't add any more towns to your already busy itinerary.

If it were me:
Barcelona 4 nights (more contiguous time)
Train to Madrid 4 nights
Train to Granada 2 nights (smaller)
Train to Seville 4 nights (bigger)
Fly (save time) to Barcelona 1 night (unavoidable waste of night; next time fly open jaw)
Fly home.

Strongly second the plan suggested by @blue439 which allows adequate time for Madrid, Granada, Seville and Barcelona and, importantly, adds Cordoba. It would be a shame to miss the incredible Mezquita!

Another option would be to go directly on to Madrid on day one and end with Barcelona. Just a thought.