While an individual citizen may lose a specific job to an immigrant, as long as the work produces a valuable good or service, that worker is creating another job with the money he is paid plus the profit of his employer. Growth comes from an increase in the population plus productivity increases.
High skilled immigrants are self-selected risk takers. What greater risk is there than to leave your native country? As such, they tend to be more entrepreneurial than citizens. Many immigrants become the innovators that create the new companies that offer multiple new high paying jobs.