i'm using 2 adapters of 700mah Approx. (ofcourse i've not reversed the terminal, when i connected it this way output was a somewhat better) and also an e string,
what should i do to increase its power, so that i can cut foam at a better rate

Cheers 

Use a computer SMPS as the power supply or a bike battery. You're only giving it about 1.4A which is not enough. You need a lot of current (not just voltage) to pass through that wire to make it hot.

if i'll use a d or g string(any string with more cross sectional area, will it work better?)

theoretically r=pl/a, so its should decrease,

but i've got many advices to use a thicker string

Thinner strings = finer cuts and lesser sagging while cutting. use a spring to reduce sagging of wire.

Increasing the current will give you a significant performance boost.

I use a transformer 24v output gives impure dc current which ensure uniform temperature of cuttingwire if I use a 24v battery which gives constant dc voltage the current in wire does not fluctuate like in the case with transformer so the temp of wire keeps on increasing and wire is red hot and breaks
so in 1st case the cutting is good

Girish bhai's suggestion of using a computer SMPS PSU is your best deal. A used PSU from an old computer could be cheaper than a transformer or a wall adapter.
But since these PSUs can supply more than the desirable current, you must get your wire length and other parameters right. I'm sure you know that bit.

I wanted to make a PWM controller, but then I figured something that's a far simpler than the hassle that comes with custom electronics.

I have a "table type" hot-wire cutter, on end of the wire is grounded and the excess length of the wire is swirled around the cantilever column which basically acts as my controller. I use an alligator clip connected to +12V to increase or decrease the conducting length of wire and thereby, controlling the temperature of the wire.

Good luck!

There are many ways to control the currents in the wire

care to enlighten us ?

@saikat sir,
Be prepared for electrifying response.

well.... I use the E String and my 12 V inverter battery for heating up the wire.  I has strung up my wire across a bamboo bow so it remains tight in all cases.... see my pictures for the wire cutting in my posts