Much depends on the type of mulch you are planning to use. If you can get a fineground mulch as landscaper's supply and shovel it lightly over the plants you probably won't harm them. I'd actually wait a few weeks and then toss the shovelfuls from the row sides when your raspberry stems can withstand the force of the tossed mulch. You might need to level it around the plants by hand. I've commonly used stump grindings that have larger wood pieces included and I have already applied it to regrowth at the stage you are at. I found that although you break some raspberries over there are others that regrow to replace them.

We have a patch of everbearing red raspberries, that I started from transplant seedlings 12 years ago. The best time for digging up raspberries and moving them around is late March/early April, when they are just barely green. The transplants quickly recover, and take off, when they are transplanted in early spring. Sometimes I will dig out and remove a plant later in the season, to reduce overcrowding, or to give me a place to stand so I can pick the ripe fruit. In the fall, I cut our patch down to 10 inches, and clean it up. Since we are getting fruit well into October, the final clean-up is done in November. I am mulching the patch, in the fall, with 8 or 10 inches of shredded tree leaves, from a maple tree we own. These leaves will disappear over the following growing season, so I think they are feeding the raspberry canes. Our patch is very vigorous, and sends out volunteer plants into the lawn, every year. I think that raspberries can be transplanted in the fall, but I have not actually done this myself.

Are these new plants this year? Assuming yes I would cut the raspberries to the ground after they go dormant in the fall, then remove the plastic. (assuming red raspberry) My experience with raspberries is they will crowd out most weeds once you get them established, and that only take the first year. The blackberry being a 2yr cane, I would wait until buds start opening next spring, then take a knife and cut up the plastic as needed to remove. My Black berries don't crowd out the weeds as well as my raspberry, but I don;t feel any need to protect it from weeds. For black berries, pinch off the top of each shoot when they get like 4' tall and they will grow thicker bushes, rather then tall and gangly. the new branches will need pinched as they try to get really tall also.

Watering = trying to stick to once a week with deep watering. But it's been raining a lot over the last few weeks up here in MA so not that much irrigation. But sometimes I water twice a week when it gets hot as the lawn is relatively new. I dont think its a water issue. Mulch mow = yes. So I did cut it more than 50% twice in a row (with 3 weeks gap in between each time). I just havent had the time and its been raining a lot so I couldnt mow. So it's possible the clippings are causing heat/lack of sun damage. But this dead grass underneath started a while back already, so its possible the mulching isnt helping, but I dont think its the root cause. Fertilizer = yes, once this year in April. Scotts with crabgrass preventer. Shade = in the mornings from home, but from around midday it gets full sun until 7-8pm. Sun isnt an issue here. If anything, the lawn gets hit by heat in the height of summer, being exposed for so long. Not sure what species this grass is (I think Kentucky Blue), but it doesnt do well in heat. But again, sun isnt an issue here. Other = I did put down compost in April. The grass was pretty covered, but emerged as a rich green. It looked fantastic. I'm not sure if it may be doing something to the lawn now though, a few months later? Any other thoughts? I really would like to fix this. I'm worried about all my hard work going down the toilet. Every day I see more of these spots. Thanks.