I would try staking it first to see if you can make it look presentable that way... its a 50/50 chance that it may regain its strength after a couple weeks to be able to stand alone again. You can leave it staked if it doesnt or you can cut it back just far enough so it stands upright by itself. It wont hurt it other than to reduce the height of the plant which probably wont grow back this season. cutting it back in spring is intended to clear away the old dead grass from the winter to make way for the new growth. then you need to address why this happened. There are a few things to consider...

1)not enough sunlight will cause tall grasses to become floppy. you may not have as much sunlight in that bed as you think. some sun grasses do quite well with partial shade etc but this one really requires major major sun to keep going strong. take a day when you are home all morning and afternoon and monitor it every three hrs starting around 8 am. take notes. it wont hurt for you to try it just to definitely rule it out. i had to move one floppy grass 3 times before i found the best spot for it.
2) too much fertilzer. i dont know if you fertilized or not but most grasses dont require fertilizer and it is known to cause floppy growth.
3) did you have a severe rainstorm that beat the grass down? certain growth habits of grasses are more susceptible to this than others..such as feather reed grass, indian grass, switch grass, etc. but I think the purple fountain grass is tall and soft bladed enough to be susceptible too.
4) this one does not apply to you since it is a new plant but some of the miscanthus will flop badly when they are mature 5-7 yr old plants. dividing is the cure for that issue.
as far as watering... its true that less water will cause it to be shorter but it also might cause it to die lol so be careful about shortchanging the water. but what happens is it stunts the growth.. it wont correct too much height after its already gotten too tall.
extra watering should be given during the grass's first summer season to help it get established. every 5 days is a good regular schedule in my zone for a new grass... but in yours I would think a bit more often would be in order especially if you havent also received regular rainfall.

sue
the one thing all gardeners share in common is a belief in tomorrow