We construct the world-line superfield massive superparticle actions which preserve 1/4 portion of the underlying higher-dimensional supersymmetry. The rest of supersymmetry is spontaneously broken and realized by nonlinear transformations. We consider the cases of N=4->N=1 and N=8->N=2 partial breaking. In the first case we present the corresponding Green-Schwarz type target superspace action with one κ-supersymmetry. It is related to the superfield action via a field redefinition. In the second case we find out two possible models, one of which is a direct generalization of the N=4->N=1 case, while another is essentially different. For the first model we formulate Green-Schwarz type action with two κ-supersymmetries. We elaborate on the bosonic part of the superfield action for the second model and find that only in two special limits it takes the standard Nambu-Goto form. In the general case it is determined by a fourth-order algebraic equation. The characteristic common feature of these new superparticle models is that the algebras of their spontaneously broken supersymmetries are non-trivial truncations of the general extensions of N=1 and N=2 Poincare D=4 superalgebras by tensorial central charges.