The road to Mendoza in Argentina runs past the resort. Try to flag down a bus or hitchhike. The hotel will organize a shuttle back to Santiago for a reasonable price.
Hitchhiking
Getting a lift on a truck is an easy prospect, as there are a constant trickle of them slowly making their way to and from Argentina. But the smaller car the faster. You'll save hours or even days! if picked up by private vehicle.
By car
The resort is easily reached from Santiago in a few hours by car. An excellent but expensive highway Ch$ 2200 total one-way for a small vehicle, possible to bypass a tunnel on the way back, saving Ch$ 1600 takes you to Los Andes, where you make to turnoff and start the climb to Portillo. The road from here is decent but often carry heavy traffic. Have chains with you in winter, when there is frequent heavy snow fall. The road is sometimes blocked by trucks failing to do the ascent to the border.
By bus
Hotel Portillo will pick you up in Santiago and shuttle you to the mountain, it's about a two to three hour trip. Also, any bus heading to Mendoza will drop you off at the resort. However be cautious because if they shut down the road due to weather they will not let a bus through, they do let the shuttles through most of the time.