If you are replacing a hot tub frame, then your old one is likely damaged, either from water, termites or some other force--be it natural or human. When you replace your hot tub frame, ensure that the new frame is better than the last by using treated lumber in wet areas, strengthening the wood framing and attaching the framing correctly to prevent forceful damage.
Remove the old, damaged frame from around the hot tub. Don't worry about supporting the hot tub. Most hot tubs are self supporting. But to be sure, remove a small amount of the framing, and look beneath to see that the tub is self supported. If not, then replace the hot tub frame one small section at a time to prevent a collapse of the tub. However, for the most part, you will not need to do so. Be careful when removing the old framing from around the hot tub. Don't scratch the tub or damage the tube in any way. This could cause the tub to leak.
Use treated lumber where water will be present. Most of the time, the floor plate should be treated, and, if the entire area around the tub is in danger of water saturation, then the entire frame should be treated. Use treated wood suited for indoor use if your hot tub is indoors.
Double up on your vertical framing members in order to strengthen the structure. Use 2-by-4s for the framing, and double them, side by side, to form a 3-inch-wide framing member--2-by-4s are 1 1/2 inches thick, so doubling them makes 3 inches. Place the framing on 16-inch centers. Even though the hot tub is not supported by the framing, a full tub of water will increase the down-pressure on the new framing, so the strength of the framing will be tested regularly.
Attach the framing using 3-inch wood screws. Slide the frame into place beneath the tub, and screw the wood screws into the floor beneath the tubs outer perimeter. Use a hand level to align the top edge of the tub with the bottom of the framing. Do not drive screws through the top of the framing and into the tub material. The corner of the framing should strengthen the entire framing apparatus; however, if you need to secure the top to the tub, do so using construction adhesive.