For 16mm rails, even 1220mm is still very long, in fact it would jump all over the place if it were a CNC router under cutting forces. On the other hand, this is a wire cutter so the forces are much lower, but I'd still be a little worried about vibration at such length, especially when cutting at the top of the Y axis where forces and inertia would be magnified (for example when changing direction, which would be more noticeable with higher accelerations). Regarding that, a good separation between the X (ground) bearings would help a lot to stiffen things up. About 30 cms between them won't hurt.
Weight shouldn't be such a big concern, in fact it adds rigidity, and a hot wire cutter cuts very slowly anyway (and stepper motors have more torque at low speeds).
What motors/drivers will you use?
Your english is not bad at all, it's quite easy to understand