Preheat the oven to 400 degrees F. Grease a baking sheet with cooking spray.
Cut the acorn squash in half; scoop out the seeds and discard. Slice the squash into 1- inch slices. Toss with the olive oil and season with salt and pepper. Place on the prepared baking sheet and roast until tender and golden brown, about 30 minutes. Remove the peel and dice the squash.
In the meantime, make the agrodolce. In a small saucepan, combine the red wine vinegar, currants and honey. Bring to a simmer, then reduce the heat to low. Cook until reduced and syrupy, about 15 minutes. Stir in a pinch of crushed red pepper.
In a large bowl, toss the squash with the agrodolce sauce, mint and almonds. Serve hot or at room temperature.